Lawrence Shankland's penalty put Hearts in front before the break
Hearts won an entertaining contest with RFS of Latvia as they kickstarted their Europa Conference League campaign.
Lawrence Shankland's first-half penalty put them ahead before the break, and Alan Forrest's strike in stoppage time sealed victory.
Hearts had goalkeeper Craig Gordon to thank at points, especially for tipping one effort on to the woodwork.
They also passed up good chances to add to their tally - including Shankland missing an empty net.
In the end it did not matter as Hearts move second in Group A behind Istanbul Basaksehir - who defeated Fiorentina 3-0 - as Robbie Neilson's side prepare to face the Serie A club home and away next.
The win in Riga keeps some hope of progression alive for injury-hit Hearts, who were handed a sixth defeat in seven games by Basaksehir last week when the Turkish side left Edinburgh with a 4-0 win.
- Hearts go from sticky patch to sizing up FiorentinaReaction & as it happened
Given that display, this was a must-win game for Neilson and his squad and at various stages of the first half they looked rattled, especially when centre-back Craig Halkett limped off 20 minutes into his return from injury.
RFS - last season's champions of Latvia who earned a shock draw in Florence in their opening match - hit the woodwork after two minutes when Gordon was at his acrobatic best to tip Emerson's shot onto the woodwork.
And the Hearts keeper pulled off another two stops in quick succession to keep his side in front just before half-time.
But Hearts were equally as dangerous in spells before the break, and had the better of the second-half without exerting total control throughout.
By that point Shankland had emphatically stroked his penalty into the top corner after Elvis Stuglis blocked Andy Halliday's cross with his arm, and missed an open goal on the stretch when Josh Ginnelly slightly overhit his pass across the six-yard box.
Nevertheless, Hearts did more than enough to earn a difficult victory, their first in European group stage football for 18 years, and made sure of it when Cammy Devlin broke free at the end before teeing up Forrest to slot home.
Player of the match - Andy HallidayHalliday was relentless in breaking up play, while also getting into the RFS box. An all-round midfield performanceHearts get reward for attacking intent - analysis
Neilson switched to a back four for this match, and signalled his intent to use Barrie McKay and Josh Ginnelly to cause problems with their direct dribbling.
It was the right approach against an inferior team, albeit one with a recent history of shocks. It paid off, too, with McKay's incredible touch and driving run instrumental in the lead up to the penalty, while Ginnelly was lively.
Halliday was also willing to drive forward from midfield and had several opportunities to score.
The commitment to pour more bodies forward clearly came with risk, but Hearts still conceded more chances than they would have liked, with Gordon rescuing them on a couple of occasions.
One gamble which did not come off was the decision to play Halkett, whose hamstring didn't hold up for even half an hour.
His absence has been harshly felt amid a long injury list, and a few more weeks out could do more damage to the team in the long run.
Overall, though, Hearts appeared to swell in confidence as the match progressed and with a struggling Fiorentina to visit Tynecastle next, the dream of qualification for the last-16 remains alive.
What they said
Hearts head coach Robbie Neilson: "It wasn't your typical European game - it was end to end. It was one both teams had to win and thankfully we have done that. We have had a difficult patch and a few injuries but the players are still confident.
"RFS are a very good side. They went to Fiorentina last week and got a draw and the majority of their players are full internationals."
What's next?
Hearts are away to Motherwell in the Scottish Premiership on Sunday (15:00 BST) before club football halts for the international break.
- Line-upsMatch StatsLive Text
Line-upsRigas Futbola Skola
Formation 3-4-3
12Steinbors92Jagodinskis21Stuglis43Lipuscek66Vlalukin28Panic24Saric25Mares81Simkovic19Ilic9Santana Deocleciano
- 12Steinbors92JagodinskisBooked at 42mins21Stuglis43Lipuscek66VlalukinSubstituted forSorokinsat 58'minutes28PanicBooked at 80mins24Saric25MaresBooked at 52mins81SimkovicBooked at 45minsSubstituted forFriesenbichlerat 59'minutes19Ilic9Santana Deocleciano
Substitutes
- 1Cerniauskas2Sorokins4Maksimenko10Rakels13Nerugals14Varslavans30Friesenbichler77Dubra99Zaleiko
Hearts
Formation 4-3-3
1Gordon2Smith4Halkett3Kingsley19Cochrane7Grant14Devlin16Halliday30Ginnelly9Shankland18McKay
- 1GordonBooked at 74mins2Smith4HalkettSubstituted forNeilsonat 22'minutes3Kingsley19CochraneBooked at 8mins7GrantSubstituted forHaringat 70'minutesBooked at 83mins14Devlin16Halliday30GinnellyBooked at 79minsSubstituted forHumphrysat 79'minutes9ShanklandBooked at 45minsSubstituted forForrestat 79'minutes18McKay
Substitutes
- 5Haring11Mackay-Steven12Atkinson13Stewart17Forrest20Neilson21Sibbick22Henderson27Smith28Clark29Humphrys39Pollock
Referee:Aleksandar StavrevMatch StatsHome TeamRigas Futbola SkolaAway TeamHeartsPossessionHome47%Away53%ShotsHome8Away13Shots on TargetHome3Away9CornersHome4Away7FoulsHome12Away10Live TextPost update
Match ends, Rigas FS 0, Heart of Midlothian 2.
90'+5'Full Time
Second Half ends, Rigas FS 0, Heart of Midlothian 2.
90'+3'goalGoal!
Goal! Rigas FS 0, Heart of Midlothian 2. Alan Forrest (Heart of Midlothian) right footed shot from the right side of the box to the bottom right corner. Assisted by Cameron Devlin following a fast break.
90'+2'Post update
Attempt blocked. Ziga Lipuscek (Rigas FS) left footed shot from the right side of the box is blocked.
89'Post update
Alex Cochrane (Heart of Midlothian) wins a free kick in the defensive half.
89'Post update
Foul by Ziga Lipuscek (Rigas FS).
89'Post update
Foul by Stephen Humphrys (Heart of Midlothian).
89'Post update
Vitalijs Jagodinskis (Rigas FS) wins a free kick in the defensive half.
87'Post update
Cameron Devlin (Heart of Midlothian) wins a free kick in the defensive half.
87'Post update
Foul by Petr Mares (Rigas FS).
86'Post update
Foul by Lewis Neilson (Heart of Midlothian).
86'Post update
Andrej Ilic (Rigas FS) wins a free kick on the left wing.
83'Booking
Peter Haring (Heart of Midlothian) is shown the yellow card for a bad foul.
83'Post update
Foul by Peter Haring (Heart of Midlothian).
83'Post update
Elvis Stuglis (Rigas FS) wins a free kick on the left wing.
82'Post update
Offside, Heart of Midlothian. Stephen Humphrys tries a through ball, but Michael Smith is caught offside.
82'Post update
Attempt blocked. Stephen Humphrys (Heart of Midlothian) left footed shot from outside the box is blocked. Assisted by Cameron Devlin.
80'Booking
Stefan Panic (Rigas FS) is shown the yellow card for a bad foul.
80'Post update
Alan Forrest (Heart of Midlothian) wins a free kick in the attacking half.
80'Post update
Foul by Stefan Panic (Rigas FS).
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Source: bbc.com