Everton's Johnny Heitinga helped break Tamworth's hearts despite a battling performance by the Blue Square Bet Premier side at Goodison Park.
Heitinga struck with a header before Leighton Baines's late penalty sealed Everton's win.
Tamworth produced a spirited display with Kyle Patterson almost equalising after a powerful run but the Lambs bowed out after Baines scored from the spot following Samuel Habergham's foul on Royston Drenthe.
Tamworth had won only one of their previous six matches since booking a trip to Goodison Park, and they found themselves behind in the opening moments.
The Staffordshire club were backed by almost 5,000 fans on Merseyside - about five times as many as turned out to witness the start of Tamworth's FA Cup adventure at home to King's Lynn in October but the rousing reception they gave their team was punctured in the fifth minute when an unmarked Heitinga was allowed to cushion a header past Joe Collister from Landon Donovan's corner.
The Tamworth keeper produced a fine stop with his feet to deny Victor Anichebe from making it 2-0 two minutes later but the Lambs soon settled and Patterson, a former team-mate of Donovan and David Beckham at Los Angeles Galaxy, went close to scoring a 29th-minute equaliser after a powerful run from the halfway line.
Everton were far from impressive but they did enough to return to winning ways after their surprise home defeat to Bolton in midweek.
Their passage into the fourth round came at a price as Seamus Coleman limped off injured in the 57th minute soon after Collister had tipped over his cross-shot.
Coleman was replaced by England international Baines, who put the tie out of sight from the spot despite Tamworth's protests at referee Robert Madley's decision.
Donovan went within inches of making it 3-0 with a superb right-footed shot from 25 yards that beat Collister but crashed off the angle of post and bar.
The final whistle saw Tamworth's players receive a standing ovation from all four sides of Goodison.
Tamworth manager Marcus Law: "There's a part of me very disappointed because we spent a lot of time on dealing with set-pieces. I've scrutinised about six DVDs of Everton, been up here for two games and that was where I felt their strengths were. Maybe the occasion and lack of focus in that first five minutes has gone against us. But it just shows you what small margins there are in football."
Everton manager David Moyes: "It was a bit of a struggle at times. Tamworth did really well and kept at it and while it was only 1-0 they were always in with a chance. We missed a few chances to make it 2-0 which would have put it to bed, but for the neutrals that kept the game running alive. While it was 1-0 Tamworth could keep running and keep trying to make things happen. "
Tamworth: Collister, Tait, Habergham, Courtney (McDonald 80), Francis, Kanyuka, Thomas (Sharif 67), Patterson, Barrow, McKoy, Christie (St Aimie 62).
Subs: Hedge, Oji, St Aimie, McDonald, Rico Taylor, Sharif, Wallen
Everton now become the N&R Road to Wembley side, our 6th team to follow this season and 2nd Merseyside one after we started with AFC Liverpool.
Everton were drawn at home to fellow Premier League side Fulham, conquerors of Charlton.