The on-loan Everton striker's scrappy goal following a corner midway through the second half epitomised a Lanarkshire derby which lacked finesse but not commitment.
Motherwell survived a late scare when Martin Canning's header drifted wide amid penalty appeals for Stevie Hammell's challenge on Flavio Paixao.
Saturday's functional victory - and fifth consecutive clean sheet under manager of the month Craig Brown - consolidated fifth place for Well. There was little chance of good football on a dreadful Fir Park pitch, which arguably is in worse condition than a year ago despite a £350,000 summer overhaul.
The goalmouths have been re-turfed but the majority of the surface is barren and cut-up, other than several small patches which were relaid after being damaged by foxes.
Hamilton handed a debut to deadline-day signing Dougie Imrie, whose Scottish Cup goal for Inverness against Motherwell last month helped ensure this rearranged match went ahead on fifth-round day.
Marco Paixao, John Sullivan and David van Zanten also came in for Hamilton, who had Simon Mensing in a three-man central defence.
Jutkiewicz saw a first-minute shot comfortably held by Tomas Cerny but there was little goalmouth action for the rest of the opening quarter. Hamilton competed well in a midfield battle but it was Motherwell who threatened next when Giles Coke fired just wide from 22 yards.
The hosts gradually got on top without seriously threatening to break the deadlock. Jim O'Brien's low cross caused some concern in the visiting defence but John Sutton could not divert it on target. O'Brien then set up Jutkiewicz with a hopeful lofted ball but the striker's shot under pressure fizzed wide.
Tom Hateley curled a 25-yard free-kick wide and Cerny got down to hold Keith Lasley's drive from similar range.
John Ruddy made his first save in injury-time when he held Marco Paixao's acrobatic volley at his near post.
Flavio Paixao replaced Joel Thomas for the second half, which began with Cerny holding Hateley's free-kick.
O'Brien injected some pace into Motherwell's build-up play and got into a dec position after a one-two with Sutton but Cerny blocked the shot with his legs.
Craig Brown made a tactical switch with Sutton dropping deeper and O'Brien given greater licence to push forward in central areas.
But Hamilton enjoyed a decent spell and Ruddy scooped Mensing's hooked effort away following Brian Easton's corner.
Motherwell took the lead in 68th minute when Jutkiewicz scrambled the ball underneath Cerny after Stephen Craigan had headed Hateley's outswinging corner into the six-yard box.
Hamilton moved Mensing into midfield and brought on former Well winger Stuart Elliott, who was applauded by the home fans, while another substitute, Kyle Wilkie, chipped over from 25 yards.
Brown introduced Chris Humphrey and Marc Fitzpatrick, but he lasted just four minutes before pulling a hamstring and being replaced by Steven Saunders.
The changes created an even more disjointed game before Motherwell dropped deep and survived some late pressure with Mensing heading over from a Wilkie free-kick before being denied by a Craigan block.
With Cerny still forward from a free-kick, Hamilton came close in the dying seconds when Martin Canning's header drifted inches wide of the far post. Mike Tumilty denied Accies a decent penalty claim when Stevie Hammell shrugged Flavio Paixao off the ball as he tried to force the ball home.