El-Hadji Diouf scored his first two goals for Doncaster as they inflicted a third straight defeat on Ipswich.
Diouf opened the scoring when he headed home James Coppinger's 18th-minute cross and then Billy Sharp made it 2-0 six minutes later.
Diouf extended the lead in the 39th minute before Ipswich hit back through Josh Carson and Michael Chopra.
It was Rovers' third win of the season, and drew them level with Coventry at the foot of the Championship table.
Ipswich have now conceded seven goals in two games, but Doncaster manager Dean Saunders will be confident his struggling side can climb out of the bottom three after a classy performance in front of goal.
Diouf showed his quality when he met Coppinger's cross before Sharp found the net a week after the death of his two-day-old son Luey Jacob.
The visitors made it three goals from three shots when Diouf struck again six minutes before the break from 25 yards out.
Teenager Carson, who came on as a substitute at the start of the second half, reacted quickest to poke home after Doncaster goalkeeper Neil Sullivan spilled Tamas Priskin's shot.
Chopra converted a stoppage time cross from substitute Jay Emmanuel-Thomas to make it 3-2, but it proved nothing more than a consolation.