Dover lifted the Kent Senior Cup at Maidstone's Gallagher Stadium on Monday.
Ross Lafayette, against his former club, and Aswad Thomas scored to bring the trophy back to Crabble for the first time since 1991.
Welling were on top in the first half and played their part in a competitive game but lacked quality in front of goal.
Dover, whose National League play-off hopes ended at Barrow on Saturday, fielded a strong side bearing just three changes from that long trip. Moses Emmanuel took Ricky Miller's place up front while Mitch Pinnock and former Welling manager Loui Fazakerley came in for Jamie Grimes and Connor Essam.
After a disappointing National League South campaign which saw them finish just four places above the relegation zone, Welling rang the changes. Among six players dropped were Jordan Brown, Phil Walsh and Rhys Murrell-Williamson, who didn't even make the bench.
Dover started well and had the first two efforts, Moses Emmanuel shooting straight at Chris Lewington before Pinnock flashed a shot just over from 20 yards.
But as the first half progressed, Welling grew in confidence and began to press forward.
Tom Richards set up Ali Fuseini for a low shot which extended Mitch Walker in the Dover goal.
Right-back Richards then hared onto a through-ball, cut inside and tested Walker again with a powerful left-footed strike.
Fuseini, having a good game in central midfield, found Dan Walker with a raking diagonal pass but when Walker pulled the trigger, he failed to hit the target.
Sam Hatton drove a low shot just wide for the Wings but Dover should have taken the lead moments later.
Pinnock's excellent deep cross from the left reached the unmarked Sam Magri but rather than head towards goal, he nodded the ball back into the middle and Welling were able to clear.
The Wings spurned a great opportunity just a minute into the second half, Cathline poking his shot straight at Walker when two of his team-mates were better placed in front of goal.
But with 54 minutes on the clock, Dover hit the front. Pinnock played into Lafayette's feet and the centre-forward turned before curling a shot high beyond Lewington's left hand.
Welling had plenty of possession in the minutes after the goal but too often their final ball lacked quality.
Eventually they did call Mitch Walker into again, Harry Crawford teeing off from 20 yards before Dan Walker saw his low drive through a crowded six-yard box beaten away by the goalkeeper.
At the other end, Dover substitute Peter Skapetis fired a bicycle kick wide after Thomas had headed Lafayette's deep right-wing cross back across goal.
Joe Healy's corner from the left then reached Magri but his header was straight at Lewington.
Jamie Slabber came off the bench late on and sent a header just wide for Welling but when Thomas headed home Healy's cross with three minutes left, it was game over.
Dover: Walker, Magri, Thomas, Orlu, Pinnock (Skapetis 74mins), Fazakerley, Emmanuel (Jackson 90mins), N'Gala, Lafayette (Stevenson 80mins), Healy, Hurst. Subs not used: Kinnear Jnr, Barnard.
Welling: Lewington, Richards, Johnson (Joseph-Dubois 71mins), Fish (Slabber 82mins), Waldren, Hayles, Fuseini, Hatton, Cathline, Crawford, Walker. Subs not used: Leacock, Francis, Agu.