John Still's side had not suffered defeat in league action since early September prior to their trip to the Pirelli Stadium, but Phil Edwards' 47th-minute looping header won it for the hosts.
Luton also had Luke Wilkinson sent off in stoppage time as they fell to third.
Victory gives Burton boss Jimmy Floyd Hasselbaink two wins from two since replacing Gary Rowett, and they are now level with Wycombe Wanderers at the top of the table.
Gareth Ainsworth's side fell behind to an early Steve Elliott strike at Cheltenham Town, but the visitors were level within a minute through Paris Cowan-Hall.
Lee Vaughan's dismissal gave Wycombe a man advantage, and they went on to secure victory thanks to goals from Steven Craig, Joe Jacobson and substitute Matthew McClure as it ended 4-1.
Shrewsbury Town missed the chance to replace Luton at the top as Exeter City came from two goals down to beat them 3-2.
Jamie Collins' first-half double appeared to have put Micky Mellon's side on course for a third successive away win in the league, but Exeter mounted a comeback after the break.
Tom Nichols halved the deficit a minute after the restart and David Wheeler levelled on 75 minutes,
Nichols then secure the win in injury time with a looping header.
Southend United were the only other side in the top six to win, a 2-1 victory over struggling Tranmere Rovers, while Plymouth Argyle and Bury both fell to defeats.
Bury suffered only their second home league loss of the season as Newport County won 3-1 at Gigg Lane, while managerless Mansfield Town reacted to Paul Cox's exit with a 1-0 win over Plymouth Argyle.
At the bottom , Hartlepool United were given early hope against York City when Scott Fenwick opened the scoring, but Russ Wilcox's side came surging back after the break to record a 3-1 win - centre-back Keith Lowe netting twice in as many minutes.
Carlisle United are just outside the bottom two after a 4-2 defeat against fellow strugglers Dagenham and Redbridge, while Oxford United were held to a goalless draw by AFC Wimbledon.
Meanwhile, Portsmouth claimed a 3-0 victory over Morecambe, Accrington Stanley beat Cambridge United 2-1 and Northampton Town edged Stevenage 1-0.
