The striker took advantage of some miscommunication in the home defence to nod home the winner following Grant Leadbitter's corner.
It was no less than the visitors deserved after they dominated a Charlton side that are still looking for their first points of the new season.
Having come into the game on the back of two defeats, Boro manager Tony Mowbray handed debuts to new £1million signing Albert Adomah and defender Frazer Richardson. Charlton welcomed back captain Johnnie Jackson from injury, while Danny Green also made his first league start of the season.
Chris Powell's side won just six times at the Valley last season in the Championship and they almost fell behind inside the first 30 seconds when Jozsef Varga tried his luck from distance and forced Ben Hamer into a save.
Boro did not look like a team lacking in confidence in the opening exchanges and some smart work from Adomah created a shooting chance for Jutkiewicz in the 11th minute, but he miscued badly.
A booking for Dean Whitehead after he seemed to elbow Yann Kermogant raised the temperature among the home fans but Charlton had nothing to show for dominating possession as the half wore on.
At the other end, Adomah saw his volley hit the bar 10 minutes before the break but referee Paul Tierney had already blown for a foul. The Ghana winger then put his free kick way over the bar to end a poor first half.
Jackson was replaced by Dale Stephens at the break and Charlton at last created a chance of note within eight minutes of the restart. Callum Harriott delivered a great cross from the left that Marvin Sordell failed to connect with, but the ball feel to Green and his shot was tipped wide by Jason Steele.
Boro responded almost immediately when Mustapha Carayol's touch teed up George Friend, who dragged his effort just wide. Jutkiewicz was next to try his luck when he shot straight at Hamer but Charlton failed to clear gave away a corner.
Hamer seemed to have it covered but a mix up with Stephens saw the ball fall to Jutkiewicz and he looped his header into the net. Green had a chance to hit back straight away for Charlton, only for Steele to parry his shot away to safety, while Stephens saw his header drift just wide minutes later.
Charlton boss Powell threw on new signing Simon Church in a bid to find an equaliser, although it was the visitors who nearly extended their lead through Carayol, leaving the final whistle to be met with boos as the hosts were condemned to their second defeat of the new campaign.