Shrewsbury had been tipped to claim a third successive win as they travelled to a Tranmere side above the relegation zone only on goal difference, though it proved a testing encounter for Micky Mellon's side.
Rory Donnelly put the hosts ahead after 29 minutes with a tidy finish from an acute angle and their lead was doubled a few moments later - Danny Holmes netting from 18 yards.
Connor Goldson pulled one back eight minutes from time, but Shrewsbury failed to find a second and Burton made the most of their slip-up at Dagenham, despite falling behind to Alex Jakubiak's 67th-minute opener.
Burton fought back thanks to goals from Adam McGurk, Abdenasser El Khayati and Damien McCrory, lifting Jimmy-Floyd Hasselbaink's side back to the top of the table and opening up a three-point gap.
Wycombe Wanderers sit two points further adrift of Shrewsbury after beating Carlisle United 3-2, but they were made to sweat by their hosts, despite taking a three-goal lead.
Kyle Dempsey and a Danny Grainger penalty in the 82nd minute ensured a nervous finish for the away side, though they ultimately held on to go four points clear of Luton Town, who lost 3-2 at AFC Wimbledon thanks to a David Connolly effort deep into second-half stoppage time.
The most impressive win of the day came at Cambridge United, as Portsmouth claimed an emphatic 6-2 triumph away from home, with Matt Tubbs' hat-trick inspiring the visitors to victory.
There was also a treble for Plymouth Argyle's Reuben Reid in their 3-1 derby defeat of Exeter City, with the visitors winning despite the 61st-minute sending off of Oliver Lee.
At the bottom of the table, Hartlepool United remain eight points adrift of safety after losing 1-0 at Bury, though they are no worse off than before the match, as York City – directly above the drop zone – lost 3-0 at Northampton Town.
Oxford United defeated Mansfield Town by the same scoreline, while three goals in the final 16 minutes ensured a 4-2 defeat at Stevenage for play-off hopefuls Southend United, and Newport County dropped out of the top seven after losing 1-0 to Morecambe.
