Michael Higdon’s 16th goal of the season after 29 minutes secured a ninth away win of the season as Stuart McCall’s side moved eight points clear of fourth-placed Dundee United.
Higdon, who scuffed an earlier opportunity, struck after Jamie Murphy’s swerving shot was parried into his path by Hearts goalkeeper Jamie MacDonald.
The triumph means Motherwell require just two further points from their final two games, at Rangers on Saturday and against United on May 13, to be absolutely certain of finishing third this season.
To deny Well, United must win their three remaining games – at Rangers tomorrow, against champions Celtic on Sunday and at Fir Park on the final day of the season.
Second-placed Rangers’ financial troubles mean they are ineligible for European competition.
William Hill Scottish Cup finalists Hearts had numerous opportunities but were unable to test Well goalkeeper Darren Randolph and missed the presence of Craig Beattie up front. They remained sixth, a point behind Sunday’s opponents St Johnstone.
It was open from the start, with Hearts fielding attack-minded trio David Templeton, Mehdi Taouil – in for Andrew Driver and Rudi Skacel – and Suso Santana behind lone striker Stephen Elliott, who replaced Beattie (hamstring).
Elliott and Jamie Murphy traded early speculative strikes before Darren Barr drove a 30-yard shot off target for Hearts.
Unchanged Motherwell were playing with confidence after their 5-1 defeat of St Johnstone and came close to taking the lead when Keith Lasley, Murphy and Higdon combined, but the latter shot tamely on the turn.
Midfielder Ian Black, who is to leave Hearts at the end of the season, failed to test Randolph and then had to be alert at the other end when Murphy rounded MacDonald and hit a weak effort from an acute angle.
After good work from Templeton – starting for the first time since the 3-0 loss at Fir Park in February – on the right side of the box, Taouil dragged an effort wide and Black failed to find the target from 20 yards out soon after.
Just as Hearts thought they were getting on top of the visitors, Higdon pounced.
MacDonald should have done better than parry a shot from Murphy, who had cut in from the right, and the ball fell for Hidgon to side-foot in.
Lasley could not connect cleanly after being played in by Hidgon on the left side of the box before Tom Hateley blasted a free-kick well wide.
Skacel replaced Taouil at half-time but still Elliott operated alone up front and the Irishman was unable to trouble Tim Clancy and Shaun Hutchinson.
Well seemed content to play on the break, but soon Hearts did threaten.
After an optimistic Santana effort, Templeton seized on a loose Chris Humphrey pass and surged into the box but Hutchinson did enough to put off the winger, who shot weakly at Randolph.
A flighted Danny Grainger free-kick from the right was then met by Barr, whose header drifted narrowly wide as Hearts came close to an equaliser once more.
A Lasley shot deflected wide off Marius Zaliukas as Well showed their danger on the break.
After Santana had a strike ruled out for offside, Humphrey’s pace almost set up a second for Well, but MacDonald scrambled to collect under pressure from Nicky Law and Henrik Ojaama, who had replaced Murphy.
Skacel rose well to meet a deep cross from Grainger, but Randolph collected comfortably as Hearts pushed bodies forward late on.
Templeton hit the side-netting in a desperate last attack but Motherwell held on.