It could have been a day to remember for teenage striker Tommy Conway, who also opened his account at senior level to cancel out Wallace's opener, but this was the only bright point for the Robins who dropped to 19th and are now winless in nine.
Millwall were ahead inside five minutes when a long ball by captain Jake Cooper led to a situation where there were three home attackers against one Bristol City defender. Wallace clinically made the most of it by advancing into the area down the right before powering a shot across Max O'Leary and into the bottom corner.
Conway should have scored his second after 28 minutes when he miscued wide after Kasey Palmer had laid the ball perfectly into his path.
Millwall were instead back in front just after the half-hour mark when Danny McNamara's cross flicked off a defender into Malone's path and he fired his effort in off the post.
The Lions were repeatedly getting in down the right, with Wallace putting McNamara through for a good chance four minutes before half-time, with O'Leary having to beat his shot away.
But it was 3-1 seven minutes into the second half, just after Bradshaw's header had been cleared off the line, as young midfielder Mitchell buried a terrific shot into the top corner.
Cooper then bent a shot high and wide, as the visitors continued to struggle to defend set-pieces and they then shot themselves in the foot to gift Millwall a fourth.
Robins captain Tomas Kalas lost control 30 yards from his own goal, allowing Bradshaw to dispossess him, run through unopposed and finish into the bottom corner to put the result to bed after 58 minutes.
It threatened to get even more embarrassing for Nigel Pearson's side as Malone lashed over from Wallace's backheel before Bradshaw headed McNamara's cross straight at O'Leary.
The season cannot end soon enough for the Robins, with Antoine Semenyo dragging a shot wide from 25 yards in the final 10 minutes to round off a miserable afternoon for them in south London.