The game grew increasingly bad-tempered as four Northampton players were booked, but the away side were able to secure the narrow victory and put them just three points from safety with five matches to play.
Meanwhile, the Pilgrims now face an uphill task to secure themselves a place in the top seven.
Exeter City's slide towards danger continued with a 2-0 defeat away at Bury, with goals from Chris Hussey and Tom Soares securing the victory for the Shakers against the 10-man Grecians, who had Danny Coles sent off in the second half.
Southend United struck twice in three second-half minutes to nullify Cheltenham Town's lead and win the game 2-1, thanks to goals from Barry Corr and Kevan Hurst. The result means that The Shrimpers remain in the playoff zone on 62 points.
Elsewhere, Chesterfield and Newport County played out a 1-1 draw, a result that sees the Spireites lose further momentum in their promotion ambitions, while Fleetwood Town recorded a 2-0 win away at Oxford United to gain further ground at the top.
In other results, AFC Wimbledon and Bristol Rovers played out a 0-0 draw, Mansfield Town won 1-0 away at Morecambe, Portsmouth recorded a 1-0 victory against Hartlepool United, Rochdale and York City ended in a goalless draw, and Wycombe Wanderers won 2-0 against Dagenham & Redbridge.
Results in full: Accrington Stanley 0-1 Northampton Town, AFC Wimbledon 0-0 Bristol Rovers, Burton Albion 1-0 Plymouth Argyle, Bury 2-0 Exeter City, Cheltenham Town 1-2 Southend United, Chesterfield 1-1 Newport County, Morecambe 0-1 Mansfield Town, Oxford United 0-2 Fleetwood Town, Portsmouth 1-0 Hartlepool United, Rochdale 0-0 York City, Torquay United 0-1 Scunthorpe United, Wycombe Wanderers 2-0 Dagenham & Redbridge