Town had taken a 14th minute lead through leading scorer Nicky Ajose only for Crewe to take a 3-1 lead into the break thanks to goals by Brad Inman and Ryan Colclough.
Jon Obika pulled one back just after half time and Town levelled through Ben Nugent’s 52nd minute own goal before Ajose's last-minute winner.
The win means that Town complete the double over Crewe for the season and now move into 14th place in League One on 34 points from 26 games.
Luke Williams kept faith with the same starting line-up as the Southend game although there was a change on the substitutes' bench with Club Captain, Nathan Thompson included after his injury layoff.
The Robins were awarded a free kick when Obika was tripped from behind about 25 yards from goal and up stepped Anton Rodgers to send in a curling effort which was pushed away by Crewe 'keeper, Ben Garratt and the loose ball eventually reached Ajose but his shot was deflected away from goal by fellow striker Obika and the chance was gone.
Brandon Ormonde-Ottewill sent in a good cross from the left wing which was almost deflected into his own goal by Crewe’s Nugent but the ball went out for a corner and when that was taken, Robert’s powerful shot was pushed away by Garratt for another corner. Jon Obika then went close with a header from close range with the 'keeper beaten but the ball went wide of goal.
Town’s continual pressure led to the opening goal in the 14th minute when Brad Barry picked up a ball from Robert on the right hand side of the penalty area and his pass to the middle of the six-yard box was fired home by Nicky Ajose for his 13th goal of the season.
Out of nowhere a back-header by Turnbull was intercepted by Brad Inman and he fired home past Town 'keeper Vigouroux to level the scores in the 20th minute.
James Jones was cautioned for a foul in the 25th minute but Town managed to lose possession and allowed Ryan Colclough to fire home from ten yards in the 26th minute to put the visitors ahead.
Ormonde-Ottewill earned another corner for the Robins in the 34th minute but that led to Rossi-Branco heading wide.
Crewe went further ahead in the 40th minute when a Crewe counter-attack saw the Town defence outnumbered and Brad Inman was given the freedom of the penalty area to fire past Vigouroux.
Town made a good start to the half after a move started by Rodgers in midfield saw the ball crossed to the far post where it was sent back over by Robert for Jon Obika to head home from close range in the 48th minute to lift the spirits of the Town fans in the crowd of 6,888. The goal was Obika’s 9th of the season.
The momentum created by the goal led to Town getting an equaliser in the 52nd minute when Crewe’s Ben Nugent turned Ormonde-Ottewill's cross into his own net under pressure from several Town forwards.
Oliver Turton was cautioned in the 62nd minute for a late challenge but the resulting cross from the free kick was easily caught by the 'keeper, Garratt.
Anton Rodgers tried his luck with a curling shot from 30 yards which only just went wide of goal with the 'keeper beaten and Yaser Kasim also sent a fiery shot in from close range which was parried.
Brad Barry tested the 'keeper’s responses in the 75th minute with a superb shot which the 'keeper parried and the ball only just evaded Obika and Nicky Ajose had a good chance shortly afterwards but his shot went straight at Garratt who gathered the ball cleanly.
Nathan Thompson made a welcome return in the 80th minute replacing Brad Barry who received good applause after a good performance for the Robins.
Both sides were going all out for the fourth goal and Town had two good chances in the space of a minute with Obika firing straight at the keeper and then Rossi-Branco heading over from the corner.
Town grabbed the lead in added time when Kasim fired in a powerful shot which was spilled by the 'keeper only for Nicky Ajose to prod home from close range sparking jubilant celebrations around the County Ground.
There was just time for Brandon Ormonde-Ottewill to weave his way into the penalty area before shooting just wide of goal and that proved to be the last action of an incident packed match with Town overcoming Crewe by four goals to three.