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Goals from Ricky Wellard and Michael Bakare ensured Welling reached the second round of the FA Cup on Saturday.
But they were made to work hard for their victory by a robust Barwell side who could have easily gained at least a replay.
There was always an edge to the tie, perhaps created by Barwell captain Richard Lavery's needless barge into George Porter after six minutes when the hosts had already been given a free-kick by referee Steven Rushton.
The first chance fell to the hosts but Barwell forward Iyseden Christie's header was well saved low down by keeper Michael McEntegart.
The hosts enjoyed plenty of early possession but Welling defended well and took their while to get into the game.
Welling could have led from their first serious attack after 18 minutes when Porter, back in the side after a month out through injury, went clean through. His right-foot shot was saved by the legs of keeper Liam Castle and Reece Harris was denied a certain goal from the rebound when defender Liam Kay bravely blocked his effort.
Barwell could have taken a 24th-minute lead but Ant Carney volleyed wide from close range at the near post after Eddie Nisevic advanced largely untroubled down the left-wing.
Welling opened the scoring on 34 minutes. Porter was threaded through on the edge of the penalty area and when his shot came back to him via the inside of the post, he picked out Wellard to slide home from inside the six-yard box.
The Wings should have been 2-0 up just three minutes later when Harris broke down the left-wing. His cross was perfect for Porter who was clearly tripped as he shaped to shoot but neither referee Rushton or his perfectly-placed assistant saw anything wrong.
Barwell came out all guns blazing at the start of the second half and it needed two excellent Sam Corne blocks to deny the hosts a clear sight of goal.
Kay should have equalised nine minutes after the break when a free-kick fell perfectly for him on the edge of the six-yard box but he shot horribly over when it seemed easier to score.
Welling should have wrapped the game on 66 minutes when Wellard picked out Harris to send him clean through. He opted to be clever instead of going for power and his weak chip was the easiest shot keeper Castle will save all season.
Barwell pushed bodies forward late on but they lacked quality when it needed most and Welling broke forward with good effect late on.
The game was settled in stoppage time when substitute Michael Bakare burst through and, after the keeper saved his first attempt, he followed up to bundle the ball home.
Welling: McEntegart, Jefford, Chambers, Porter, Wellard, Taylor, Lokko, Corne, Harris, Williams, Vidal. Subs: Osborne, Kabba, Gagliardi, Adeyinka, Cumberbatch, Obafemi, Bakare.
Barwell: Castle, Lower, Nisevic, Kay, Towers, Lavery, Tomkinson, Woodward, Christie, Hickey, Carney. Subs: Towers, Gaunt, Wakeling, Brennan, Hartopp, Punter, Hadland.
Attendance: 843.