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Welling booked their place in the FA Trophy first round draw after a derby win over Tonbridge on Sunday.
Strikers Tom Whitnell and Andy Pugh were both on target as Wings boss Jamie Day made it two wins out of two in charge.
On-loan Gillingham striker Pugh, pictured, put Welling ahead midway through the first half, firing home after good work by Loui Fazackerley.
Whitnell doubled Welling's lead in the 37th minute when he collected Ryan Johnson's pass and chipped the ball beyond keeper Lee Worgan.
Tonbridge pulled a goal back minutes later when they were awarded a penalty for handball and leading scorer Carl Rook tucked away the spot-kick.
Pugh twice went close to adding to his tally while Jamie Cade missed a good opening for the visitors.
Welling made the game safe with 13 minutes left when Whitnell was again set up by Johnson and he fired in at the near post.
Tonbridge pulled one back in stoppage time when Rook's challenge on Mitten went unpunished and he slotted home the loose ball but, by then, it was too little too late.