Former Boro striker King struck from 12 yards 12 minutes from time to make Tony Mowbray's team pay after Lita's spot-kick on the half hour had been saved by Keiren Westwood.
The home side started well as Clive Platt's header was saved by Jason Steele after five minutes, then Gary McSheffrey tested the goalkeeper with a left-foot shot from 20 yards.
Lita was the first Boro player to threaten, missing a header from Joe Bennett's cross in the eighth minute.
A scrappy period of play followed with neither side able to gain the upper hand - James McPake marshalling the Coventry box consistently, frustrating the visitors.
City's Lee Carsley miscontrolled a Richard Keogh cross and smashed over from inside the box, before Marlon King and McSheffrey brought saves out of Steele from free-kicks.
The home side continued to dominate and Boro could only muster a weak header from Scott McDonald which failed to test Westwood.
However, Boro's confidence grew as they outpassed their hosts and Julio Arca curled a wicked 25th-minute shot in from the left wing which Westwood had to tip around the post at full stretch on 25 minutes.
Tony McMahon could have scored with a strong header from the resulting corner but his header went wide.
Boro were given a great chance to take the lead when Lita was fouled by Nathan Cameron in the box - but the striker's blast down the middle was blocked in spectacular fashion by Westwood.
Coventry started the second half with purpose and McSheffrey was unlucky not to hit the target with a drilled shot from the right.
Arca continued to threaten for Boro with crosses and shots from the left, before Lita went close again 10 minutes after the restart when his header from Marvin Emnes' cross went wide.
Discipline was poor throughout with the scrappy fouls creating a stop-start rhythm which benefited neither side as the game entered the final quarter.
Michael Doyle shot over the bar from distance in the 74th minute as the hosts wrested back some control of the match - and their hard work paid off when Matthew Bates fouled McSheffrey. King took his chance from the penalty spot.
Mowbray replaced Arca with Kris Boyd as he sought an equaliser, with McSheffrey making way for defender Jordan Spence.
The visitors pumped crosses into the Coventry box - but to no avail as Adrian Boothroyd's team held firm.