A fine run off his wing from Bradshaw almost created a third as he found Sonni-Lambie in space in the box, his effort hitting the post before Ngumoha's rebound was saved by Gracey.
Cam Williams was back at left-back and played a fine ball down the line to put Ngumoha away into the box but his effort was deflected into the side-netting.
Bailey Hall denied Mane as the half ticked to a close but the Reds failed to heed the warning and the same player was sent away to finish clinically for a 2-1 half-time score.
Mane was still a threat in the second period and ran past several players before being finally blocked out as Wolves sought an equaliser.
But it was Liverpool who stretched their lead to two again on 64 minutes as Bradshaw grabbed his first via a deflected shot following a Sonni-Lambie pass.
Lucas Clarke had arrived off the bench for Liverpool and the centre-back made an early impact as he cleared a header off the line, after a Wolves free-kick was headed back across goal.
Furnell-Gill should have grabbed a second goal with 12 minutes remaining but his free header from Williams' delivery was saved by Gracey once again.
Nguhoma deserved a goal for his relentless energy and he should have had it with three minutes left when he was sent away with just Gracey to beat but the goalkeeper continued his fine afternoon with a save.
Myles Dayman collected a second yellow card for Wolves on the stroke of full-time but the visitors still had time to pull a goal back, with Wilcox heading home a corner.
If that could have caused nerves among the home side, it didn't show and Bradshaw completed the scoring to continue his own fine form with a beautiful clip over Gracey from Sonni-Lambie's decisive pass.
**Team**
Hall, Cisse, Williams, Furnell-Gill, Pitt (Clarke, 57), Upton, Bradshaw, Onanuga (O'Connor, 46), Sonni-Lambie, Ahmed, Ngumoha.
Unused subs: Bernard, Lonmeni, Martin.
Goals: Sonni-Lambie (23), Furnell-Gill (29), Bradshaw (64, 90+5)
**Next up**
The U18s do not play again until 2025, with a trip to Nottingham Forest in the U18 Premier League their first outing of the New Year.
That game is scheduled for a 12pm GMT kick-off on Saturday January 11.