Goals from Filipe Morais and Dougie Imrie had taken Caley Thistle to the brink of SPL safety but, with results going their way elsewhere, Well substitute Sutton fired home from close range.
Inverness had fought back well from Brian McLean's opener and former Motherwell striker Richie Foran had a shot cleared off the line in the final 10 minutes.
Before Sutton scored, Inverness were on their way to safety as both St Mirren and Falkirk could not have caught them, with the bottom two still to meet.
Despite being so close to safety, Caley Thistle are now only three points off the bottom with two games left.
The point sealed seventh place for Motherwell, and perhaps more importantly they did not pick up any yellow cards in their bid for a Europa League spot via the Fair Play league, even after the 53rd-minute introduction of Maros Klimpl, who has been booked nine times this year.
Motherwell goalkeeper Graeme Smith entertained the disappointing 2,818 crowd early on with a courageous diving header 35 yards off his line after initially heading the ball away from Foran as the former Motherwell striker chased a long ball. The ball broke for Imrie but Mark Reynolds easily cleared his shot off the line.
Grant Munro was off target with a header and Morais had a low drive comfortably saved as Inverness pushed forward in the opening 15 minutes.
But the hosts took control and Keith Lasley curled just wide from 20 yards at the other end after clever passes from McLean and Jamie Murphy.
McLean, signed by Butcher in 2006, boosted his chances of winning a new contract in the 26th minute when he headed Steven Hammell's corner in off the near post of Michael Fraser, who will join Motherwell in the summer.
David Clarkson fired a first-time shot wide after the ball broke 20 yards out and McLean headed into the side-netting from a tight angle following Hammell free-kicks.
Inverness levelled against the run of play in the 40th minute when Imrie beat Hammell and cut the ball back for Morais to drill into the corner from eight yards.
The visitors started the second half with a good edge to their play and Smith did well to push a powerful Morais volley past his post after the ball broke for the Inverness midfielder.
Imrie put them ahead in the 56th minute with a brilliant finish from eight yards. Lionel Djebi-Zadi won the ball from Paul Quinn just inside the box and stood up a cross to the back post where the former Clyde forward volleyed into the roof of the net with his left foot.
Inverness stayed on top and Morais fired wide from distance before Imrie had a low drive saved at Smith's near post after bursting into the box.
Clarkson volleyed just wide from 18 yards after Ian Black's poor headed clearance as Motherwell came back into the game.
And the hosts levelled in the 79th minute. Clarkson cut the ball back for Maros Klimpl whose weak effort was helped into the roof of the net by his fellow substitute from five yards.
Reynolds cleared off the line moments later after Foran had helped the ball over Smith following a long ball and the former Fir Park man volleyed high over from a snapshot.
Jim O'Brien had a late chance to leave Inverness firmly in danger but his first-time effort from 40 yards drifted wide following Fraser's sliced clearance.