MATT GLENNON made three penalty saves and still finished on the losing side as Town's slim play-off hopes were all but extinguished.
The Town stopper denied Ryan Lowe in the 43rd minute and in the 79th, saved spot kicks by Gary Roberts, then Julien Baudet when referee David Foster ordered a retake because of encroachment.
The unfortunate Glennon was beaten by David Mirfin's own goal in the 45th minute and a 69th-minute Lowe shot which took a cruel deflection off Aaron Hardy as Crewe hit back after Chris Brandon's fine strike midway through the first half.
Had there been any justice, Glennon would have scored an equaliser when he ventured upfield as Town pounded the Crewe penalty area late on.
But the visitors, who to their credit, defended very well throughout, held out to leapfrog Peter Jackson's side, who are now 13th in League I.
It was Town's second successive home loss, and fifth of the season, and just as against Brentford seven days previously, they paid dearly for failing to take chances.
Against the Londoners, Andy Booth was the most guilty.
On Saturday, new loan signing Paul Hayes did everything but score.
The Barnsley striker looked especially lively in the first half, twice turning neatly on the edge of the box to fire in right footers, the first of which, in the 10th minute, struck the base of Crewe keeper Ben Williams' right-hand post.
It was all Town in the opening 25, in fact, with Andy Taylor testing Williams with a sixth-minute volley before Hayes hit the woodwork from Gary Taylor-Fletcher's pass.
When Frank Sinclair played in a low ball on 17, Hayes again turned centre-back Danny O'Donnell, standing in for the injured Billy Jones, only for his shot to go just wide.
Brandon's 22nd-minute effort, however, was bang on target.
Mirfin won the header from Glennon's drop kick, Taylor passed to Taylor-Fletcher, and Brandon took possession just outside the area to curl a low left-footer past Williams and into his right-hand corner.
It was his first goal since his penalty sealed a 1-0 home win over Blackpool on February 14 last year.
But the midfielder was unable to add a second when, from another good position, he blazed a 32nd-minute shot way off target.
Crewe's first effort had come in the 26th minute, when Glennon grasped Lowe's powerful low shot at the second attempt.
Then after 37, they were denied when Luke Beckett cleared Roberts' close-range poke off the line.
When Mirfin felled right-back Danny Woodards to concede penalty number one, Glennon halted Lowe's low drive with his feet.
But Town still succumbed before the break when Tyne and Wear whistler Foster played good advantage when he looked set to award a free-kick for a challenge by Michael Collins on Ben Rix.
With the Crewe midfielder prone, teammate O'Donnell played the ball up to Roberts, from whom Luke Varney took possession wide out right and crossed.
Mirfin and Mike Higdon rose, with the Town man deflecting the Crewe striker's header in at the near post.
It was a big lift for Crewe, but Town still dominated the opening stages of the second half.
Taylor-Fletcher shot just too high from Hayes' neat 49th-minute lay-off, then put a free-kick over after Woodards' 53rd-minute foul on Brandon, who was playing at the top of a midfield diamond.
Hayes hooked a Matt Young cross over the top on 62 minutes, then five minutes later, somehow flicked the ball too high when Collins' fierce shot was blocked.
Those misses were made all the more frustrating when Glennon was wrongfooted as Hardy went in to tackle as Lowe shot from 20 yards.
Visiting keeper Williams pulled off a fine one-handed save as Hayes floated an effort in from Brandon's lay-off.
Then came the penalty - Sinclair admitted he fouled Varney but said it was outside the area - from which Glennon performed more heroics.
How they rated:
Matt Glennon Pulled off three great penalty saves and could do little about either Crewe goal. Didn't deserve the defeat. Rating: 8/10
Aaron Hardy Stood in for the suspended Andy Holdsworth at right-back and did well. Unlucky with Crewe's second goal. Rating: 7/10.
Andy Taylor The Blackburn left-back worked hard to impress against the side where he had a spell on loan earlier this season. Rating: 6/10
Frank Sinclair The second-half foul which referee David Foster viewed as being inside the penalty box was his only lapse. Rating: 7/10
David Mirfin With a penalty concession and an own goal, it doesn't look too good, but did plenty of positive things too. Rating: 6/10
Gary T-Fletcher Spoiled another busy display with the needless late caution (dissent) which brings a one-match ban. Rating: 6/10
Michael Collins Worked hard and tackled strongly on the right side of the diamond, but some passes went astray. Rating: 6/10
Chris Brandon Back in midfield after his frontline foray at Rotherham. Looked busy and scored a fine first goal of the season. Rating: 7/10
Matty Young Playing on the left of midfield, never held back and put in plenty of running. Has impressed of late. Rating: 7/10
Paul Hayes The Barnsley loan man seemed full of intent on his Town debut and was pretty unlucky not to mark it with a goal. Rating: 7/10
Luke Beckett Never got the kind of chances he feeds off, but toiled manfully and made a couple of good defensive clearances. Rating: 6/10
David Foster could have awarded Crewe a free-kick close to their own box but instead played advantage. A three-man upfield move ended with Mike Higdon's header being deflected in by the unfortunate David Mirfin, left. The 45th-minute equaliser came soon after the first missed penalty.
Spotlight on the ref:
Tyne and Wear whistler David Foster was good in parts, not so in others. On the positive side, he kept the game flowing, played the advantage well for Crewe's opener and got the first penalty right. But Frank Sinclair insisted the second was outside the box and few would have ordered the retake. Also got in the way too often.
Crewe Alexandra: Williams, Woodards, Baudet, O'Donnell, Moss, Roberts, Cox, Rix, Lowe (Jack, 90mins), Higdon, Varney. Subs Not Used: Tomlinson, Pope, Carrington, Coo.