Nicky Maynard, the latest in a long production line of talented players from the Crewe Alexandra Academy, proved the difference between the two sides at Gresty Road.
Cheltenham didn't play badly, although the defensive mistakes that have crept into recent performances have still not been eradicated, and it was Maynard's sharpness in front of goal that consigned the Robins to their third successive defeat. At the other end there were chances for Cheltenham to get back into it but goalkeeper Ben Williams was usually in the way.
The position at the bottom of Coca-Cola League One therefore tightened further but with Gillingham only taking a point from their visit to Bristol Rovers the results were not disasterous.
Robins boss Keith Downing made two changes to his team with Alan Wright and Ashley Vincent both fit again after injury. Andy Gallinagh and Andy Lindegaard stepped down to the substitutes bench and the rest of the squad was the same as that which took on Walsall last week.
Cheltenham, who were backed by a healthy following of travelling supporters, began with the five man midfield that has been employed for recent away games. Steven Gillespie started wide on the right and Vincent on the left with Paul Connor as a lone striker.
Crewe pushed three men up front from the start including leading scorer Nicky Maynard and former Bristol City trainee Joe Anyinsah, who is currently on loan from Preston North End.
Cheltenham had the first decent chance of the game with only five minutes played when Gillespie cut in from right and his low drive was beaten away by goakeeper Ben Williams. The ball rebounded off Gillespie for goal kick.
Anyinsah for Crewe and Craig Armstrong for Cheltenham both sent shots wide during an open start to the game in which both sides found plenty of space to play.
And with 14 minutes played the scoring was opened when Crewe launched a quick breakaway after a Cheltenham attack. Maynard found Kenny Lunt wide on the left and he side-stepped a challenge from Gillespie before angling a ball into the penalty area. Maynard took it with his back to goal but was allowed the space to turn and shoot inside the far post from a 45 degree angle.
Maynard almost doubled the lead only moments later when Stephen Schumacher found him with a through ball but Shane Higgs was out quickly to block with his legs.
Cheltenham regained some composure and Scott Brown saw a shot deflected wide then almost scored from the resulting corner. His in-swinging flag kick looked to be going in until Williams clawed it out from under the bar. Cheltenham kept the pressure on but when a chance fell for Gillespie, his lob shot went over the bar.
Cheltenham were enjoying a good spell mid-way through the first half and when David Bird supplied Gillespie just inside the box, the striker extended Williams with a lob shot that the goalkeeper stretched to grab at the second attempt.
Vincent and Gillespie swapped sides for the minutes leading up to half-time but it was the home team who almost scored again right at the end of the half when Crewe captain Julien Baudet saw a heavily deflected shot cleared off the line by Vincent.
Cheltenham began the second half brightly with Vincent sending a long shot wide and a promising cross from David Bird evading the goalkeeper. Gillespie arrived at the far post but unfortunately the ball took a high bounce on the hard ground and sailed over his head.
A swirling wind began to whip up around the ground and Crewe began to experience some difficulties with their passing game.
Cheltenham kept pressing forward and got into a series of promising positions without being able to turn them into scoring opportunities.
However, there was always a danger that Crewe would be able to attack on the quick breakaway and won two free-kicks in promising situations just outside the box, the second resulting in a booking for Wright.
Thankfully for the Robins, both Baudet and Lunt smashed their free-kicks into the stand behind the goal and a deserved equaliser for Cheltenham arrived in the 62nd minute and it was a fine goal from Gillespie.
Richard Keogh knocked a ball out wide to the left and Wright's cross was headed down by Vincent. Gillespie collected it on the edge of the box and sidestepped a defender before beating Williams with a delicious chip shot.
The goal brought the Cheltenham supporters to life and although some tension began to creep into the home stands, their nerves were calmed again on 68 minutes when Tom Pope got into the Cheltenham area and showed great determination to keep going despite the attentions of the Cheltenham defence.
Eventually the ball ran free to Maynard, who swung his boot at it and Higgs was left stranded as the ball nestled inside his left-hand post.
Cheltenham switched to three up front with Gillespie and Andy Lindegaard alongside Connor but the contest was decided in the 76th minute when Lunt's corner was headed towards goal by Baudet and Maynard completed his hat-trick by deflecting the ball over the line from close range.
Deep into injury time Williams made a magnificent save from Gillespie when he volleyed a Connor cross at goal but the only really good news for the Robins in the closing stages was a goal for Bristol Rovers at the Memorial Stadium that pegged Gillingham back to 1-1.
CREWE ALEXANDRA (4-3-3): B.Williams; Abbey, Baudet, McCready, Boyle; Roberts (Carrington 90), Lunt, Schumacher; Anyinsah (Morgan 68), Pope, Maynard (Jones 90). Subs not used: Fon Williams (Gk), O'Donnell
CHELTENHAM TOWN (4-5-1): Higgs; Gill, Keogh, Duff, Wright; Gillespie, Bird, S.Brown (D'Agostino 88), Armstrong (Connolly 77), Vincent (Lindegaard 68); Connor. Subs not used: S.P.Brown (Gk), Gallinagh
REFEREE: A.P.D'Urso (Essex)
ATTENDANCE: 5,279