Full-time from The Den
Captain for the day Williams struck the only goal of a fiercely competitive game with 14 minutes on the clock to settle this affair. It was just the response manager Neil Harris had demanded following the disappointment of both the performance - and result - at Fleetwood on Tuesday.
Harris had shown two changes from that team, bringing in Ed Upson and Fred Onyedinma for Joe Martin and Steve Morison, the latter of whom had been unwell on Friday.
It took a magnificent double save from Lions keeper Jordan Archer to deny Peter Clarke's goal-bound bullet of a header in the opening couple of minutes as Bury started on the front foot.
The Lions weathered the early storm and a superb pass from George Saville picked out Onyedinma on six minutes, but the latter's effort was claimed by Daniel Bachmann in the Bury goal.
Williams and the tireless Lee Gregory combined in the 12th-minute and so nearly broke the deadlock, only for Gregory's header to be claimed by the increasingly busy Bachmann.
Millwall didn't have to wait much longer to edge ahead, and when Onyedinma teed up Williams, the skipper struck a low 25-yarder from the right flank that flew beyond Bachmann's reach and into the bottom corner.
Midfielder Saville lashed the ball over from distance with another long range effort and Gregory steered a header narrowly wide of the target as The Lions continued to turn the screw in search of a second goal.
Bury offered very little in the opening half, and when they did try to smuggle the ball to use the pace of Joseph Dodoo and power of Clarke, they found that the Lions players were hunting in pairs, snapping at their heels and giving very little opportunity to threaten Archer in the home goal.
The second-half, however, saw David Flitcroft's side start to really prise and probe, but they found The Lions well organised and superbly disciplined when pushed to the limit by a couple of crude challenges that failed to register even a yellow card.
The experienced head of Morison was introduced for Onyedinma and moments after entering the fray he released Gregory with a magnificent volleyed back-heel. Unfortunately Gregory's first touch took the ball away from him and although he managed to get in a shot, keeper Bachmann had enough time to race out and block.
Chesmain, 17, showed no signs of nerves and won his first header before crisply intercepting the ball and breaking up a Bury attack - earning roars of approval from Lions fans.
Millwall needed to stand firm under a late Bury onslaught, and did so supremely, restricting the visitors to one clear chance with 10 minutes remaining, but neither Clarke nor sub Danny Rose could get any contact on Danny Pugh's penetrating cross from the left.
In fact it was The Lions who could have put the seal on a tough, physical encounter right at the death when Williams put through Morison, but his shot was palmed away by Bachmann..
Bookings: Webster (72mins), Saville (73mins)
Scorer: Williams (14mins)
Bury: Bachmann, Riley (Pope, 66mins), Hussey, Clarke, Etuhu, Clarke, Mayor, Jones (Rose, 37mins), Soares, Cameron, Dodoo (Pugh, 69mins). Subs not used: Ruddy, Nardiello, Eagles, Brown.
Booking: Cameron (71mins)
Ref: D. Whitestone
Att: 8,311 (away 456)