Yaser Kasim gave Town the lead in the 34th minute with a superb free kick and the victory was sealed by Andy Williams’s second half goal in a match watched by 6513 at the County Ground.
Louis Thompson was included in the Town starting line up having served a one match ban for being sent off at Crawley while Massimo Luongo missed out due to a tight hamstring.
There was one minute's prematch applause for ex Town player George Hudson who died recently aged 90. George made over 400 appearances for the Club from 1948 to 1960 and had also been inducted into Town’s Hall of Fame.
Swindon kicked off playing towards the Town End on a bright sunny afternoon and had an early chance to attack through Nathan Byrne who laid the ball off to Andy Williams but his first time cross was overhit.
Crewe’s first attack in the 7th minute resulted in a free kick when Lee Molyneux was tripped 25 yards from goal but Jamie Ness’s shot struck the defensive wall and went out for a corner.
Nathan Byrne was looking lively down the right wing for the Robins always looking to run at the visitors defence and also swung over a couple of good crosses without being able to find a Town player.
Yaser Kasim tried his luck from 25 yards with a powerful freekick which flew over the crossbar with the keeper scrambling across his line.
Town’s best attack so far came in the 22nd minute when Williams won the ball in his own half and passed the ball to Gladwin who slotted it forward to Byrne on the edge of the area but his low shot was saved by Crewe keeper Garratt and the ball was hoofed away by a defender.
Louis Thompson had two good chances to score in the space of a minute with his first effort from the edge of the area which was saved by Garratt and the second opportunity being set up by Gladwin’s backheel.
Brad Smith was also denied by a superb save made by Garratt with the Crewe keeper putting in a fine performance to keep the Robins at bay so far.
Swindon were awarded a free kick in the 33rd minute for a foul 25 yards from goal in a central position and there was a break in play while Ness received treatment before Yaser Kasim stepped up to score his first goal of the season with a superb curling shot to the right of Garratt in the 35th minute.
Crewe replaced Ness straightaway with Chris Atkinson before the match restarted and the visitors then went in search of an equaliser.
Andy Williams did well to trick his way into the penalty area before firing in a low cross from the right which just needed a touch but the ball evaded the Town players before a defender hoofed the ball clear in the 43rd minute.
Town had another good attack down the right with Byrne passing the ball to Gladwin who stepped inside and fired a powerful shot which Garratt caught and there was just time for a Town corner which came to nothing and the referee ended the half with Crewe just about to launch an attack down the right wing.
Swindon’s first attack of the second half saw Ben Gladwin collect the ball on the left wing before advancing into the penalty area and crossing to the backpost where Michael Smith was penalised for fouling a defender while challenging for the ball.
Town almost went ahead in the 55th minute thanks to the efforts of Brad Smith who crossed from the left hand side of the area for Michael Smith to outjump the defence but his header struck the crossbar and the ball bounced down only to be cleared by a defender.
Brad Smith earned a corner for Town in the 64th minute when his cross was deflected behind but the short corner routine came to nothing and the ball was cleared. The Robins were awarded another corner shortly afterwards when Michael Smith chased down a defender who was forced to knock the ball out of play and although the resulting cross was weak, the ball was cleared to Louis Thompson but he mishit his shot and the ball trickled out for a goal kick.
The referee awarded a free kick to Town some 35 yards from goal when Louis Thompson was fouled and up stepped Kasim to fire in another superb curling shot which Garratt did well to tip over for a corner in the 70th minute.
Wes Foderingham made a rare mistake shortly afterwards when he misjudged the flight of the ball from a high cross but fortunately the Town defence spared his blushes and cleared the ball.
Crewe were now showing more ambition in attack having pushed Town back into their own half as the match passed the midway point and then having withstood the pressure, Andy Williams did well to earn another corner for Town which led
Andy Williams scored his second goal in as many games after receiving the ball on the edge of the penalty area and he coolly advanced before slotting the ball to the right of Garratt to double Town’s lead in the 77th minute.
The goal had given Town an extra spring in their step and they continued to pass the ball around well deep in Crewe’s half for several minutes but a misplaced pass eventually gave the ball back to Crewe.
Brad Smith left the field to good applause when he was substituted by Jack Barthram in the 82nd minute.
Vadaine Oliver replaced Marcus Haber and Bradden Inman replaced Moyneux in the 84th minute with Crewe struggling to make any impact.
The Sponsor’s Man of the Match award was announced as Yaser Kasim who had sealed a fine performance with the superb opening goal.
Ben Gladwin was substituted by George Barker as the match entered added time and the Town midfielder also left the field to good applause for his efforts but there was little time for the substitute to make any impact before the final whistle.
The win moves Mark Cooper’s team onto 7 points from 4 games played and they now look forward to hosting Brighton at the County Ground in the Capital One Cup on Tuesday 26th August.