The forward made it five goals in his last three starts in bitterly-cold conditions at the Training Centre as the team registered a fifth win in seven matches in the Elite Group.
Tom Huddlestone returned to action with a 45-minute shift and Tom Carroll played 60 minutes.
Playing with a strong wind behind them in the first half, the lads slowly built pressure before opening the scoring in the 23rd minute.
Wesley Atkinson made a double block to deny Carroll and Shaq Coulthirst, Nabil Bentaleb was denied by goalkeeper Luke Daniels and we then struck the woodwork twice in as many minutes as Grant Hall's header from Carroll's cross clipped the top of the crossbar before Carroll's 20-yarder flicked the left upright.
The deadlock was broken midway through the half as Carroll drove a low pass into Coulthirst, he touched it into the path of Munns who made no mistake with a sure sidefoot finish into the corner.
West Brom were always tidy in possession and created half-chances in the first half - Kemar Roofe might have done better from Adil Nabi's cutback. Nabi later shot wide from Scott Allan's pass and then shot straight at Jonathan Miles from the edge of the box.
Milos Veljkovic replaced Huddlestone for the second half as our midfield continued to impress.
We doubled the lead on 54 minutes as Carroll released Nathan Byrne down the left and his low cross was fired home at the far post by Kenny McEvoy.
Five minutes later and Munns was there again for 3-0, taking full advantage of a fantastic pass from Carroll to pick him out centrally in the penalty area. Munns, in space, controlled and drilled high past Daniels.
Giancarlo Gallifuoco replaced Carroll on 62 minutes and delivered the pass of the day for the fourth goal.
Picking up the ball just inside the Baggies' half, Gallifuoco clipped the ball between defenders into the path of Coulthirst, who controlled on his chest and blasted home.
A fine goal to complete a good afternoon's work.
Spurs U21: Miles; Fredericks, Fryers, Hall (Stewart, 75), Byrne; Bentaleb, Huddlestone (Veljkovic, 46), Carroll (Gallifuoco, 75); McEvoy, Coulthirst, Munns. Unused sub: Vigouroux.
West Brom: Daniels, Francis (S Nabi, 62), Smart, Birch, Atkinson, Jones, Roofe, Allan, Sawyers, A Nabi, Brown. Unused subs: McCalla, Lewis, Wedderburn, Barrow.