But Lincoln's superior finishing proved to be the key as second-half goals from Jamie Clarke and Aaron Brown settled the contest.
"I watched Telford play against Solihull on Tuesday night and I knew it was going to be a difficult game, especially being away from home," said Sutton.
"A 1-0 lead is never comfortable in football and they scored a decent goal to get them back into the game before enjoying a period of pressure. We withstood that and in the end I think we deserved the victory on the balance of play.
"Telford have a decent record in the FA Cup, this is a lovely stadium and the fans get behind them so we didn't expect an easy ride at all - and we certainly didn't get one."