Arnaud Kalimuendo's second-half opener for Forest was cancelled out by Utrecht substitute Mike van der Hoorn before Jesus stepped off the bench to fire the visitors' late winner.
Forest bounced back from last weekend's disappointing defeat at Everton to secure their third win in this season's competition - their first on the road - and move to 11 points after six matches.
Murillo, Oleksandr Zinchenko and Douglas Luiz returned from injury as Sean Dyche made nine changes from Saturday's 3-0 loss and his re-jigged side made an impressive start to the first competitive meeting between the teams.
Callum Hudson-Odoi forced Utrecht goalkeeper Vasilios Barkas into a low save and Zinchenko wasted a golden chance in the 11th minute when he fired wide following Dan Ndoye's neat flick inside the penalty area.
Forest defender Morato's header was diverted over the crossbar and Luiz's curling effort was turned away by Barkas.
Utrecht did not test Forest's replacement goalkeeper John Victor - Matz Sels was sidelined due to a groin injury - until the 24th minute when Miguel Rodriguez's long-range effort was saved in the top corner.
That triggered a spell of pressure for Utrecht and although Victor was not troubled again before the break, it was a more even contest.
Forest made another quick start in the second period as Kalimuendo broke the deadlock in the 52nd minute.
The former Rennes striker wriggled clear of three defenders on the edge of the area and after a lucky rebound, buried an angled left-footed finish inside the far post.
The Frenchman almost struck Forest's second seven minutes later, bundling a close-range effort against a post following a corner, before Nicolas Dominguez fired straight at Barkas.
But Utrecht levelled with a rare chance of their own, and through questionable Forest defending, when the unmarked Van der Hoorn ghosted in at the far post to head home Souffian El Karouani's free-kick in the 73rd minute.
The home side's confidence soared and a partisan home crowd sensed a winner, but it was Forest who had the last word.
Ndoye's thumping header from Hudson-Odoi's left-wing cross was well saved by Barkas, but substitute Jesus turned home the rebound just a minute after replacing Kalimuendo.
Barkas' sprawling save kept out Hudson-Odoi's fizzing shot before Siebe Horemans blazed Utrecht's hopes of a stoppage-time equaliser high and wide.
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