James Henry's 13th-minute cross evaded United goalkeeper Mark Howard to give the leaders the advantage and the same player also struck the post before setting up Dave Edwards to secure the points shortly after the interval.
The match kicked off at 1:25pm to commemorate United's landmark, but Nigel Clough's men could not mark the occasion as their eight-game unbeaten run in League One was halted.
The visitors took a sixth-minute lead through Callum Wilson's close-range effort, and Brentford's Alan Judge had a penalty saved before Clayton Donaldson, Marcello Trotta and Alan McCormack chipped in to spare his blushes.
Third-placed Leyton Orient lost ground on the top two as they required Nathan Clarke's deflected half-volley to salvage a 1-1 draw at Walsall.
Rotherham prevailed 1-0 over Peterborough through a Kieran Agard penalty as fifth played sixth at London Road, and Steve Evans' men leapfrogged Preston North End to go fourth - their rivals beaten by the same scoreline at Swindon Town.
Hayden Hollis bagged a brace either side of half-time and Ronan Murray had also scored for County, before James Berrett offered Carlisle a route back into the match that Gary Liddle’s 70th-minute overhead kick definitively closed.
Crewe Alexandra profited from Carlisle's misfortune as they climbed out of the bottom four courtesy of a 3-1 win at Gillingham inspired by Chuks Aneke's double.
Graham Westley's side were downed in similarly dramatic circumstances - Dean Lewington scoring the last of three goals in the final 10 minutes as play-off chasing MK Dons prevailed 3-2 in remarkable fashion.
