Darren Ferguson made a winning start as Doncaster manager with Keshi Anderson's late goal sealing a 2-1 victory at Shrewsbury.
There were just three minutes left when Anderson, on loan from Crystal Palace, drilled home a powerful shot from eight yards after being set up by Cameron Stewart.
Doncaster earlier raced into a 14th-minute lead with captain James Coppinger keeping his cool to drill home a left-footed shot from 12 yards after a blocked shot from Richie Wellens kindly ran his way.
Shrewsbury goalkeeper Jayson Leutwiler also needed to be alert to tip a Stewart free kick over the bar while he then came charging off his line to keep out a Nathan Tyson shot with his legs.
But Shrewsbury responded well to falling behind and nearly equalised when Sullay Kaikai's 20-yard drive was saved by Thorsten Stuckmann and Larnell Cole's follow up hit the post.
The leveller the hosts threatened arrived in the 27th minute with defender Nat Knight-Percival powering home a near post header from Liam Lawrence's corner.
Shrewsbury might have been in front by the break but Stuckmann just managed to divert a stinging shot from Cole which moved in the air wide.
Kaikai and Cole both missed good chances for Shrewsbury in the second half before Anderson fired the winner to clinch a first away win of the season for Doncaster.