The Sky Blues are up to sixth in SkyBet League Two after a brace from Jordan Ponticelli helped Mark Robins' side to a hard-fought 1-2 win over Crawley.
Ponticelli gave City the lead after just four minutes when he fired low into the far corner from just inside the area.
Lewis Young did draw Crawley level ten minutes later but Ponticelli was on target yet again with ten minutes to go when his exquisitely curler found the bottom corner.
City are up to sixth with four games left to play.
It was evident from Robins' squad selection that the Sky Blues were heading to West Sussex to attack, and they had the lead within five minutes. Marc McNulty broke free down the right before cutting back for Ponticelli, making his first start since November, to fire through the defenders legs and into the bottom corner.
Ponticelli's goal away at Notts County last weekend was met with an instant impact from the home side, and Crawley nearly gave the 1,200 City fans behind the goal deja vu when Thomas Verheydt tested Lee Burge from range, but the 25-year-old did well to parry the ball away.
Crawley were level after twelve minutes, however. Young was given enough time to stride onto the ball in the area and send a low effort across Burge and into the bottom corner. 1-1.
Jonson-Clarke Harris hasn't scored in four for the Sky Blues but almost changed that just before the half-hour mark. Young's sloppy pass conceded possession to Clarke-Harris who rifled an effort goalbound from 25-yards that was forced over the bar by Glenn Morris in the Crawley net.
Liam Kelly was gifted a golden opportunity to restore City's lead just before half-time. Clarke-Harris again won possession in the final third and foud Kelly on the edge of the area but the 28-year-old's shot was easily saved.
After the break Kyel Reid and Max Biamou entered the fray as the Sky Blues looked to play with slightly more width, with Ponticelli and Reid hugging the touchlines.
Biamou's introduction was putting the Crawley defence under pressure and forcing mistakes. The Frenchman's interception on the edge of the area was worked through to McNulty as he raced in from out-wide but his shot was saved brilliantly from close range by Morris.
McNulty's new role behind the striker was creating opportunities as the Sky Blues came close twice to retaking the lead. First, the former Pompey man almost found the bottom corner with an audacious bicycle kick from Ponticelli's cross, but the ball bobbled wide, before his fellow Scotsman Jack Grimmer watched his effort blocked.
It wasn't long before City were back ahead though. Ponticelli must have felt like the most patient man in Coventry waiting for his chance the lead the line for the Sky Blues and he made is three goals in two games with ten minutes to go. The teenager watched as the Biamou's pass rolled into his path for him to curl into the far corner in style.
Attendance: 3294 (1197 away)
Goals: Ponticelli (4'), Young (12'), Ponticelli (77')
Yellows: Tajbakhsh (28'), Doyle (63')
Coventry City XI: Burge (GK), Grimmer, Willis, McDonald, Haynes, Bayliss (Reid 56'), Kelly, Doyle (C), Ponticelli, McNulty, Clarke-Harris (Biamou 66').
Subs: O'Brien (GK), Davies, Stokes, Shipley, Barrett.
Crawley Town XI: Morris (GK), Young, Connelly, Bulllman, Yorwerth, Tajbakhsh (Doherty 60'), Smith, Payne, Boldewijn, Ahearne-Grant, Verheydt (Camara 58').
Subs: Mersin (GK), McNerney, Roberts, Randall, Sanoh.
Referee: Lee Swabey.
Assistants: Stuart Butler, Kevin Howick & Louis Marks.