Saido Berahino gave the Cobblers the perfect start with a goal inside the first minute, firing home the rebound after Kelvin Langmead was denied by Ross Atkins.
However, Cleveland Taylor equalised straight from the restart when he drilled home a low shot past Shane Higgs, who was making his Northampton debut.
The home side regained the lead in the 12th minute when Langmead was pulled back by Ryan Austin and Michael Jacobs despatched the ensuing spot-kick. Six minutes later Northampton had captain John Johnson sent off for a challenge on John McGrath.
Billy Kee and Aaron Webster went close for Burton, before substitute Chris Palmer equalised for a second time on the hour when he rifled a shot into the top corner after Calvin Zola did well to lay the ball back.
Langmead almost put Cobblers back in front with a header that just failed to find the target. But with two minutes of normal time left, Langmead was penalised for a foul on Taylor and Richards scored from the ensuing spot-kick.