Scottish Premiership Wrap: Motherwell, Hibs play out thriller, Kilmarnock overcome lowly Hearts
Stuart McCall's side had earlier surrendered a two-goal lead at Easter Road, but Sutton scored his second of the match in the second minute of injury time to ensure a share of the spoils.
Sutton opened the scoring on 12 minutes, before on-loan winger Lionel Ainsworth doubled the advantage with an angled drive shortly before the half-hour mark.
The hosts' were trailing by just one at the break, however, thanks to Jordon Forster's strike, and a Michael Nelson header that found its way home via the crossbar levelled the scores on 76 minutes.
Just three minutes later former Kilmarnock striker Paul Heffernan completed the turnaround for Terry Butcher's men for what appeared to be the winning goal.
Yet, there was time for one last twist as Sutton grabbed his second of the match.
The result leaves Motherwell third, while Hibernian remain outside the top six in seventh.
There were also six goals at Rugby Park, as Kilmarnock defeated beleaguered Hearts 4-2.
Danny Wilson's own goal put the hosts ahead, but Dale Carrick's clever lob restored parity on 30 minutes.
A quickfire double from Kris Boyd shortly after the break put Kilmarnock in charge, however, and, though Sam Nicholson pulled one back, Michael Gardyne made sure of the points for Allan Johnstone's men.
Kilmarnock sit eight in Scottish Premiership table, while Hearts remain 20 points adrift of safety, having incurred a 15-point deduction at the start of the season.