Rovers netted three goals in the second half but they were indebted to a fantastic goalkeeping performance from Marko Marosi.
The Slovakian shot-stopper superbly denied both Ben Coker and Simon Cox in a first half dominated by the Shrimpers.
But Rovers took control after the break and opened the scoring in the 51st minute with John Marquis firing home from close range.
Six minutes later, Mallik Wilks sent a 20-yard shot into the bottom right-hand corner of the net before a tame Tommy Rowe shot trickled in to make it 3-0 in the 70th minute.
Southend responded with Tom Hopper reducing the arrears in the 75th minute before Marosi again did well to deny both Sam Barratt and Sam Mantom.
The keeper was finally beaten again in the 86th minute when substitute Theo Robinson fired home from close in.
But the Shrimpers were unable to complete a comeback as Doncaster held on for the points.
“That’s what it’s all about,” McCann said. “I said it to the players - that’s the way I play.
“We’ve come to a team that are probably one of the best teams in the league at home and Chris Powell’s record speaks for itself, and we’ve absolutely dominated them in the second half.
“Of course we had to ride a wave for 35 minutes in the first half when we were relying on our back four, relying on Marko Marosi who was unreal and pulled us out of it.
“And when you’ve got the threat that we have at the other end of the pitch with Wilks and Marquis, you can hurt teams.
“I’m really pleased that a corner routine we’ve worked on came off. It should have been James Coppinger on the end of it but he wasn’t on the pitch so Tommy took it on his right foot.”