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Bradley Goldberg scored a first-half hat-trick as Welling eased into the fourth qualifying round of the FA Cup on Saturday.
Welling led 3-1 at the break and their task was made easier in the second half when the Western League visitors had two men sent off.
Goldberg had an early header straight at keeper Josh Oak but his finishing was clinical thereafter.
There were 16 minutes on the clock when Nathan Green played him in behind a static Tavistock backline and Goldberg fired home from the angle with his left foot.
Tavistock had a couple of half-chances through Ben Cross and Luke Brown but Welling gave themselves some breathing space with two goals in five minutes.
A shocking error by Cross left Goldberg with the freedom of the penalty area to slot home his second on 35 minutes.
He claimed the matchball five minutes later, finishing off a neat move by finding the far corner again - this time with his right foot.
Tavistock got themselves on the scoresheet a minute before the break, Jack Crago's delightful 20-yard right-foot shot giving keeper Dan Wilks and earning applause from many home fans inside Park View Road.
Tavistock's discpline let them down within a minute of the restart. Cross' afternoon went from bad to worse as his awful challenge on Danny Waldren correctly resulted in a straight red card.
While Tavistock held on gamefully with 10 men, they made life even harder for themselves on 66 minutes.
There was no need for full-back Josh Robins to make a challenge, let along a two-footed one on Connor Dymond. Amazingly, the visitors questioned referee Callum Walchester's red card. It was another correct decision by the man in black.
The game now being played almost exclusively in the Tavistock half, Welling added a fourth with 15 minutes left, substitute Aaron Cosgrave's run forward finally finished off by Josh Oyinsan, who recorded his first goal for the club.
Goldberg's golden touch in front of goal failed him in the last 10 minutes as he blazed over from close range and was then twice denied in quick succession by Oak.
Welling: Wilks, Dymond, Anderson, Widdrington (Jebb 68mins), Swaine, Okosieme, Cook, Waldren, Goldberg, Coombes (Oyinsan 68mins), Green (Cosgrave 68mins). Subs not used: Copeland, Agyemang, Rich-Baghuelou.
Tavistock: Oak, Cross, Robins, Evans, Daw, Burns (Hallett 82mins), Prynn (Cairo 73mins), Crago, Watson, Suanley, Brown (Cloke 45mins). Subs not used: Watson, Greening, Roberts, Hawes.
Attendance: 491.