Former Tamworth striker Adam Cunnington scored a first-half penalty against his former club to help extend Cambridge United's unbeaten start to the season.
Luke Berry, who was fouled to win the spot-kick, doubled the U's advantage with a tap-in after Lambs goalkeeper Cameron Belford denied Nathan Arnold.
Berry scored his second in eight second-half minutes with a glancing header from Harrison Dunk's cross.
The Lambs finished with 10 men after Jordan Rose was shown a second yellow.
The visitors' best chance came before Cunnington opened the scoring, with a fingertip save from Chris Maxwell denying Wayne Thomas's close-range effort.
Midfielder Ryan Lloyd was rushed into Tamworth's starting side after his one-month loan move from Port Vale was announced minutes before kick-off at the Abbey Stadium.
VIEW FROM THE DRESSING ROOM
Cambridge United boss Richard Money told BBC Radio Cambridgeshire:
"You need different types of victories to do well in this league. On a day when people expect you to win sometimes it's just not that easy. Tamworth have a history of being difficult opponents, they take points from a lot of teams, they've already taken points from Wrexham and Barnet.
"It's another benchmark victory in a different way for us, that we can get the right result on a day when people probably expected us to win and by and large it was relatively comfortable.
"In these types of games, you've got to be good when periods of the play are not what you really want and I think then when you get the opportunity to play, hopefully your quality comes through, but you've also got to be good at those moments when it's a little bit scrappy.
"On days like today it's up to the players to lead it from the pitch. The last thing you want is supporters getting frustrated. You hope the quality of your play and the excitement of your play will lift the support base and then the atmosphere becomes what you want it to be."