The Sky Blues remain winless this season but will be buoyed by the result against early pacesetters Boro.
Marvin Emnes' first-half strike looked enough to give the home side all three points and six consecutive victories for the first time since 1995.
But Jutkiewicz's goal proved otherwise as Boro substitute Faris Haroun missed a golden chance to score the winner in the final seconds.
Middlesbrough boss Tony Mowbray made four changes from the side that beat Peterborough in the Carling Cup on Wednesday, with on-loan Carl Ikeme, Rhys Williams, Julio Arca and Justin Hoyte all returning.
Coventry manager Andy Thorn stuck with the same eleven that picked up the club's first point of the season at home to Watford last weekend.
The home side almost took the lead after eight minutes through Hoyte. He took advantage of Chris Hussey's error to go through on goal but could only power his effort against the top of the crossbar.
Middlesbrough made the breakthrough in the 21st minute through top scorer Emnes. Coventry defender Chris Hussey tried to clear but could only divert the ball into the path of the Dutchman, who finished clinically for his seventh goal of the season.
The visitors missed a golden chance to equalise in the 26th minute through striker Roy O'Donovan. He controlled Matthew Bates' missed interception but could only sidefoot the ball over the bar.
Boro almost made it two on the stroke of half-time, first through Emnes, whose goalbound effort was blocked by Cranie following a 40-yard dribble, and then through Joe Bennett, whose 18-yard effort was well tipped over by Joe Murphy.
Coventry enjoyed plenty of possession following the restart and defender Richard Keogh should have levelled in the 58th minute, but he could only head Sammy Clingan's corner over the bar with the goal at his mercy.
Boro almost put the game beyond doubt eight minutes later when full-back Hoyte was put through on goal following Emnes' clever backheel but failed to test Murphy.
The home side were made to pay 14 minutes from time when the Sky Blues grabbed a deserved equaliser. Hussey's dangerous cross landed at the feet of O'Donovan. His shot was parried by Ikeme but the ball fell to Jutkiewicz who headed the rebound in off the underside of the crossbar.
The home side tried desperately to grab a late winner and almost did so through Haroun. He rose high and cannoned his header against the bar. Goalkeeper Murphy smothered the loose ball to secure the point for his side.