Swindon started well but couldn't score in the first half. However it was Shrewsbury who took the lead on 40 minutes when Fortune-West beat the offside trap and only had Phil Smith to beat which he did to make it 1-0 to the away side.
Barry Corr equalised for Swindon on 67 minutes and a corner the ball finally fell to him and he headed in from close range.
On 73 minutes Christian Roberts headed Swindon into the lead from close range for his 13th goal of the season.
Jerel Ifil picked up a late yellow card which was his 10th of the season so he will now be suspended for 2 games.
Shrewsbury appeared to equalise late on when the ball seemed to have crossed the line, but the goal wasn't given so Swindon stayed in the lead.
Overall it was a fairly average game, but a very important win for Swindon who now move back into the top 3 with a game in hand over Rochdale which is being played on Tuesday night.