The goalkeeper's finest moment came in stoppage time when he saved a penalty from Derek Asamoah. Craig Hinton's foul on Asamoah earned him a second yellow card.
In spite of reaching the Johnstone's Paint Trophy final earlier in the week, Rovers' play-off chances are fading as this was their fourth league game without a win.
Both sides created decent opportunities during the opening 15 minutes and Rovers' lively striker Rickie Lambert tested home keeper Chris MacKenzie with a low shot.
Then Asamoah wasted an even better chance for the Shrews when he screwed his shot across the goalmouth and the wrong side of the post.
The visitors stepped up the pressure midway through the first half. Midfielder Lewis Haldane got round the back of the home defence and forced MacKenzie to save well at his near post.
Then four minutes later, Lambert cleverly made space for himself just inside the area but his goalbound shot was deflected away for a corner.
Shrewsbury responded with two well-flighted free-kicks by Marc Tierney causing havoc.
Leo Fortune-West headed the first free-kick against the far post. Then Phillips was forced to make a fine save after Tierney found the head of Dave Edwards.
The Shrews made a bright start to the second half and impressive midfielder Stewart Drummond twice went extremely close within the space of three minutes.
Firstly he shot wide from the edge of the area and then saw his goalbound header tipped away for a corner by Phillips.
The visitors were restricted to the occasional breakaway but they nearly scored against the run of play when substitute Richard Walker shot wildly when well placed.
The home side had much the better of the closing minutes and it needed more good work by the man of the match Phillips to deny Asamoah on three occasions in open play.
In stoppage time, Asamoah surged into the box only to be fouled by Hinton. The referee waved a yellow card at Hinton for the second time and Rovers were down to ten men.
Asamoah picked himself up and took the penalty but his weak kick was comfortably saved by Phillips.