It took the home side just four minutes to break the deadlock and it came via loan signing Landon Donovan.
The USA international produced a searching cross and Johnny Heitinga was on hand to head home from close range. It might have been two moments later, but Joe Collister pushed a Victor Anichebe effort round the post.
Tamworth showed some neat touches, however, and almost brought the tie level with a strike from Scott Barrow, but it drifted just wide of the left-hand post.
Tamworth continued to pass the ball and Kieron St Amie went close after 63 minutes with an effort from distance, but it drifted just wide.
Everton continued to look the most likely, however, and Donovan might have done better when he found himself unmarked after 65 minutes.
Everton continue their league campaign against Aston Villa next weekend, while Tamworth host Wrexham.