Grant Holt's 16th league goal of the season from the penalty spot inside the opening 45 seconds was cancelled out by Albert Adomah in the second half, before Lansbury and Surman fired the Canaries into the automatic promotion places.
The home side extended their unbeaten run to seven league games and opened up a three-point cushion over third-placed Swansea after what turned out to be a nervy last 20 minutes.
The loss signalled the end of a four-match winning streak for the visitors.
Norwich took just 45 seconds to open the scoring as a long ball up field from Zak Whitbread was firstly flicked on by Holt and then helped into the path of Wes Hoolahan by Simeon Jackson.
The playmaker advanced into the area and was clumsily brought down by Liam Fontaine for a penalty.
Holt made no mistake from the spot, smashing the ball into the top corner, giving former England number one David James no chance.
James' opposite number, John Ruddy, was tested by a 25-yard Nicky Maynard strike before Jackson, who scored twice against the Robins at Ashton Gate earlier on in the season, turned smartly on the edge of the area before failing to direct his snap shot on target.
Norwich should have doubled their advantage after 34 minutes when Russell Martin delivered a dangerous ball across the face of the goal but Jackson failed to convert.
The visitors went up the other end and could have levelled but Ruddy pushed Adomah's fierce drive to safety.
The dangerous Jackson broke through the Robins defence five minutes after the interval but did not have enough power in his shot to beat the out-rushing James, while Adomah once again stung Ruddy's palms with a powerful drive from distance.
Adomah, who was twice denied by Ruddy in the first half, finally made the home side pay after 65 minutes against the run of play when substitute Jamal Campbell-Ryce broke clear at pace and fed the midfielder, who placed the ball under the diving Ruddy to equalise.
James was called into action when he had to be brave to deny Crofts after his initial punch fell into the midfielder's path before Holt headed wide from a Hoolahan cross.
The home side went ahead in the 88th minute as substitute Lansbury raced through the Robins defence to place past James
Then Surman slotted home from close range to ensure Norwich picked up their 10th home win of the season with a third in stoppage time.