Scunthorpe were left with nothing to show after dominating most of the second half at Glanford Park.
With both teams still looking for their first points of the season, it was the visitors who made a flying start with a goal after just 60 seconds. It was a stunning 35-yard effort from striker Adam Leitch-Smith that dipped over home goalkeeper Sam Slocombe into the far corner of the net.
Scunthorpe responded well and were rewarded with a 15th-minute equaliser from summer signing Mike Grella who netted from close range after a header from centre-back David Mirfin had crashed back off the crossbar.
The home side nearly snatched the lead before half-time when striker Bobby Grant headed across the face of goal from a Josh Walker corner. On the hour it was Grant again who missed another great chance when he climbed to meet a left-wing cross from Callum Kennedy but headed over the top.
Scunthorpe were unlucky not to get their noses in front in the 67th minute when Jimmy Ryan rattled a post with a fierce shot from 10 yards with keeper Alan Martin well beaten.
Crewe, who had been on the back foot for much of the second half, then threw on loan signing Harry Bunn from Manchester City for his debut. And the 19-year-old made an immediate impact with a key part in the build-up that saw Luke Murphy pop up unmarked in the box to squeeze his shot past Slocombe for the winner after 73 minutes. Byron Moore almost made it 3-1 when he forced his way into the box and fired against the outside of the near post.