The visitors had themselves missed a spot-kick when striker Noel Hunt's tame effort was saved by Joe Murphy on 20 minutes with the scores at 1-1.
The home side had taken the lead after two minutes through winger Gary McSheffrey but Royals striker Simon Church's clinical finish eight minutes later ensured their lead did not last long.
It proved to be the final moment of note until Jutkiewicz blazed his 93rd-minute spot-kick over.
The Sky Blues made an explosive start and went in front courtesy of McSheffrey, who fired home from an acute angle after being played in by David Bell.
But the visitors equalised after 10 minutes, a flowing passing move resulting in Adam Le Fondre rolling the ball to striker partner Church who swept home from inside the box.
Experienced Royals winger Jobi McAnuff then danced into the penalty box and drew a foul from 18-year-old defender Cyrus Christie.
But Murphy ensured the scores remained level, diving to his left-hand side to repel striker Hunt's tame effort.
That lifted the home crowd and their team responded by coming close to re-taking the lead, defender Chris Hussey firing over the rebound after Adam Federici had palmed out the impressive McSheffrey's shot on goal.
Reading re-asserted their authority and came close through McAnuff
and Joseph Mills, but Murphy ensured the two sides went in level at half-time.
Coventry started the second half brightly as McSheffrey came close to grabbing his and his side's second of the game, but Federici was equal to his long-range effort.
A sweeping move then almost gave Jutkiewicz the chance to restore Coventry's lead, but a fine defensive header from Kaspars Gorkss denied him with the goal at his mercy.
Sammy Clingan was next to go close, but his 30-yard free-kick was well saved by Federici.
Reading responded by bringing on Hal Robson-Kanu and the move almost paid dividends within a minute, but he failed to hit the target with his close-range header.
McAnuff then had a decent effort well-blocked by Bell, and it took an importance clearance from Richard Keogh to clear the danger from the subsequent corner.
Coventry came close to a dramatic late winner when substitute Clive Platt's long-range drive was saved by the excellent Federici, although it may not have counted anyway following a late offside flag from the assistant referee.
The game seemed destined to end all-square until Jutkiewicz was brought down by Gorkss following his marauding run in injury-time. He stepped up to take the kick but fluffed his lines, powering the ball way over the bar in what was the final kick of the game.