The hosts shot themselves in the foot early in the game, as Scott Dan scored an own goal to give the Tyneside club the lead.
Rovers could have levelled things up just before the break, but Tim Krul saved a David Dunn penalty to keep Newcastle in front.
The score remained at 1-0 until the last minute, when substitute Gabriel Obertan sealed the victory for the visitors with a second goal; the result lifts The Magpies above Liverpool and Arsenal in the table.
Alan Pardew was full of praise and admiration for his team, who put the disappointment of going out of the FA Cup at the weekend to Brighton behind them.
“We had a bit of criticism about the Brighton game and we lost Cabaye, the two Senegal boys couldn’t make it, and we still won,” Pardew told Sky Sports.
“Great credit to the players and particularly to James Perch. I left him out even though he was excellent at Brighton. But he came into the midfield for the second half and we looked a lot stronger in there.
“We’ve got such resolve in the squad.
“To get a win on the back of Brighton was brilliant and we can look forward now to the end of the season. We’ve got a tremendous opportunity that we want to try and take.
“We’ve gone up to fifth tonight – it’s an outstanding achievement from this football club,” the tactician beamed.
Newcastle were without the suspended Yohan Cabaye for the game, but may well be able to welcome back strike duo Demba Ba and Papiss Cisse for Sunday’s match-up with Aston Villa.
By Gareth McKnight