Saturday's success increased Well's hopes of securing European football for next season.
Scotland Under-21 striker Jamie Murphy continued his recent fine form when he put the visitors ahead in the 12th minute but St Johnstone responded well to the setback and recalled striker Steven Milne breached Motherwell's mean defence to equalise from close range in the 26th minute.
However home keeper Graeme Smith spilled substitute Lukas Jutkiewicz's shot with five minutes remaining and Sutton made no mistake from three yards out.
Milne's goal was just the second Craig Brown's side have conceded in the last 10 games as they have moved into a comfortable position in the top six as a result of their long unbeaten run.
And Sutton's late strike is a significant boost to their bid to catch Hibernian in fourth - but is a real blow to St Johnstone as they seek a second successive season in the SPL.
Derek McInnes' men are eight points clear of basement side Falkirk, who face Celtic at Sunday lunchtime, before the Bairns and St Johnstone meet in the Falkirk Stadium next weekend.
McInnes made two changes from the side which drew with Hibs. Graham Gartland returned after recovering from a chest infection at the expense of Danny Grainger and former Dundee striker Milne replaced Cillian Sheridan.
Brown was forced into one alteration to the team which defeated Kilmarnock. Jim O'Brien - having recovered from illness - replaced Jutkiewicz, whose knee injury restricted him to a place on the bench.
The in-form visitors were straight on the front foot, Chris Humphrey tearing past Steven Anderson down the right and swinging in a decent cross towards Sutton in the first minute.
Although the former St Mirren striker was eased off the ball by Dave Mackay, the move signalled Motherwell and Sutton's early intent.
Humphreys was in sparkling form in the first 10 minutes, beating Anderson for pace on three occasions and supplying dangerous crosses into the box.
And in the 12th minute Motherwell's superiority was rewarded when Murphy put his side ahead as he beat the offside trap, rounded keeper Smith - who had ill-advisedly rushed from his line - and slotted home at the second attempt after Gartland had blocked his first effort.
St Johnstone almost hit straight back when Stephen Craigan was penalised for a push on the edge of his own box and visiting keeper John Ruddy had to handle Liam Craig's free-kick cleanly with Milne waiting to pounce on any mistakes.
The home side then twice came close to an equaliser in the 21st minute when Ruddy saved well from Deuchar. From the corner Michael Duberry fired wide from 10 yards out.
St Johnstone were threatening an equaliser and it was no great surprise when Motherwell's run of three games without conceding a goal came to an end in the 26th minute as Milne rolled the ball beyond Ruddy following a clever flick from Murray Davidson caught out Craigan.
McInnes made a substitution two minutes later when he brought Grainger on for Anderson, who may have picked up an injury but who had in any case endured a torrid time against Humphrey.
Milne almost scored a second just after the half-hour mark when a terrific block from Mark Reynolds fell into his path and his shot was deflected narrowly over the bar by Craigan.
The half began with good crosses for both teams which deserved a better end product. First, Deuchar worked an opening down the right but saw Milne fail to connect with his square pass, then O'Brien and Murphy combined nicely on Motherwell's left but Sutton mis-timed his challenge for the latter's cross.
The visitors almost regained their lead 12 minutes into the second period when Murphy latched on to Keith Lasley's quickly taken free-kick and although his scuffed shot beat St Johnstone keeper Smith, Duberry raced back to hack the ball off his own line.
Brown's side were the more fluent at this stage without creating any clear-cut opportunities and in a bid to change the pattern of the game, McInnes introduced former Chelsea midfielder Jody Morris in place of Davidson 20 minutes into the half.
Brown responded three minutes later by bringing Ross Forbes on at the expense of O'Brien while Lasley was replaced by Giles Coke.
Brown played final card with 10 minutes remaining when he brought on on-loan Everton striker Jutkiewicz for Murphy.
The changes helped to inject some urgency into the away side and Jutkiewicz's shot in the 85th minute was spilled by Smith with Sutton was on hand to tap home from three yards out.
McInnes threw on Filipe Morais for Craig immediately after the goal but it was all in vain for the home side as Jutkiewicz could afford to waste a terrific chance to make the game safe in injury time as Brown's side collected all three points.