The Sky Blues are up to sixth in SkyBet League Two after first-half goals from Jonson Clarke-Harris and Tom Bayliss were enough to see City to victory.
Clarke-Harris gave the visitors the lead after just four minutes in an opening priod that could have seen Mark Robins' side extend their leads futher.
Alexandra did draw level momentarily through Jordan Bowery but Bayliss' winner before the break was enough to seal all three points.
The result lifts the Sky Blues to sixth in SkyBet League Two, five points below the automatic promotion places with a game in hand.
City had the lead after just four minutes. Clarke-Harris made the most of some obvious gaps in the Crewe midfield to casuallly saunter to the corner of the area and blast past Alex 'keeper Ben Garratt. Zoumana Bakayogo came closest to hooking the ball off the line but he failed to stop Robins' side from taking the lead.
Crewe came close to leveling just after the half-hour mark. Jordan Bowery demostrated his pace by charging down the left andd crossing for former City forward Shaun Miller, who forced a stunning reflex save from Liam O'Brien.
Alexandra were level moments later. O'Brien again pulled off a strong save from Paul Green's close range strike but it fell to Bowery who was able to calmly nod home from close range.
The home side were making it very easy for the Sky Blues to run at them, and they were punished against just before the break when Tom Bayliss mirrorred the game's opener. The teenger floated into the area before finding the far-bottom corner with the inside of his left foot to give City the lead at the break.
City started the second half the birhgter. Marc McNulty and Clarke-Harris both came close to doubling their sides lead in the opening five minutes of the first half, firing over and wide respectively.
Liam Kelly, on at half-time to replace the injured Tom Bayliss, is yet to score for the Sky Blues but came inches away from chngin that just before the hour mark when he race in on goal, rounded the final defender, but curled his shot just shy of the far post.
Jamie Sterry, another former Coventry player amongst Crewe's ranks, almost saw his cross drift into the far corner to draw crewe level with twenty minutes remining. The defender's looping attempt has O'Brien well beaten, but thankfully floated wide.
Attendance: 4,666 (1,537 away)
Goals: Clarke-Harris 4', Bowery 31', Bayliss 41',
Coventry City XI: O'Brien (GK); Grimmer, Hyam, McDonald, Haynes; Vincenti (Ponticelli 87'), Bayliss (Kelly 45'), Doyle (C), Shipley (Reid 77'); McNulty, Clarke-Harris.
Unused Subs: Bilson (GK), Stokes, Barrett, Biamou.
Crewe Alexandra XI: Garratt (GK); Ng, Ray (C), Sterry, Bakayogo (Ainley 12'); Nolan, Green, Kirk, Pickering; Miller (McKirdy 71'), Bowery (Dagnall 80').
Unused Subs: Richards (GK), Raynes, Lowery, Barlaser