The Lambs were looking to become the first non-league team to beat top-flight opponents since Sutton knocked out Coventry in 1989 but they made a disappointing start when Johnny Heitinga headed in Landon Donovan's corner inside five minutes.
Tamworth gave as good as they got after that, particularly in the latter stages of the first half, but they could not find an equaliser and Everton substitute Leighton Baines wrapped up victory from the penalty spot 11 minutes from time.
Everton boss David Moyes, with his options limited by injuries, named a reasonably strong side and handed a first start to James McFadden since his return to the club, while Toffees fan Joe Collister made only his second appearance in goal for Tamworth.
Before the match, former Everton defender Gary Ablett, an FA Cup winner with the Toffees in 1995, was remembered with a minute's applause.
The 46-year-old died of cancer on New Year's Day and members of his family and former team-mates joined the two teams on the pitch.
Ninety-four places separate the sides across five divisions but Tamworth are no stranger to the third round having also reached this stage in 2006 and 2007 while Everton have lost to Shrewsbury and Oldham during Moyes' reign.
What the underdogs needed was a good start but they found themselves behind inside five minutes.
It was not a good moment for 20-year-old Collister, who missed Landon Donovan's corner and defender Heitinga headed in via a deflection off Tamworth captain Duane Courtney.
The Premier League side were well on top early on and Collister did well to block a shot on the turn from Victor Anichebe before Diniyar Bilyaletdinov blazed over the bar from 15 yards.
McFadden also had two decent early chances to net his first goal since August 2010, first heading wide and then guiding a shot just past the post after a neat backheel from Bilyaletdinov.
Everton's dominance soon passed, and the visitors, roared on by an estimated 5,000 fans, became an increasing presence in the game.
They almost had a special goal to cheer in the 29th minute when striker Kyle Patterson set off on a run from the half-way line to the edge of the area but placed his shot just past the far post.
Patterson, a former team-mate of Donovan and David Beckham at the Los Angeles Galaxy, then shot straight at Howard as the home fans began to get a little frustrated.
What Moyes definitely did not need was more injuries, but he was forced into a change 12 minutes into the second half when Seamus Coleman limped off after seeing Collister tip over a cross-shot.
Baines came on, and at the same time Marouane Fellaini was also receiving treatment after a crunching tackle from Patrick Kanyuka, but he was able to carry on.
There had been a distinct lack of quality in the second half in particular but Everton finally put together a decent move in the 77th minute as Donovan and Baines combined to set up Bilyaletdinov for a shot that was beaten away by Collister.
And moments later the Toffees were given the chance to double their lead from the penalty spot.
Substitute Royston Drenthe did not need much help going down under pressure from Sam Habergham but referee Robert Madley was unmoved by the Tamworth protests and Baines sent Collister the wrong way.
Donovan then 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.