The home side ended the game with 10 men after Jack Lester was red carded in stoppage time.
Chesterfield started strongly but Burton came closest to scoring when a 25-yard free kick from Lee Bell in the 31st minute came back off Tommy Lee's right hand post.
But the visitors went ahead three minutes later when they broke up the left and Jacques Maghoma placed a low shot across Lee and inside the far post.
Chesterfield almost equalised in the 40th minute when Jay O'Shea's shot was flicked on by Richards but Dean Lyness scrambled the ball against the inside of his left post.
The home side laid siege to the Burton goal in the second half with Mark Randall striking a post with a 59th minute free kick and Richards heading against the far post five minutes later.
But Richards grabbed a deserved equaliser in the 74th minute when he headed home Randall's cross from the left but Lester was sent off for wrestling Zander Diamond over in added time.