Joint-manager Jimmy Albans felt Grantham Town were worthy of their 2-1 FA Cup away victory at Chasetown.
Paul Grimes gave the Evo-Stik Division One South side a first-half lead.
Richard Teesdale levelled from the spot for Chasetown before Grantham's Phil Watt was sent off on the hour, but Gio Carchedi grabbed a 68th-minute winner.
Albans told BBC Lincolnshire: "In the first half we were by far the better side. We had to weather the storm but with 10 men we've dug in and won."
After Grimes' 30th-minute opener gave Grantham a half-time advantage, Evo-Stik Premier Chasetown were awarded a 56th-minute penalty for a harsh handball against Grant Brindley, which Teesdale converted.
Three minutes later Grantham were down to 10 men when defender Watt was shown a red card for a dangerous tackle, but Carchedi pounced on a mistake by the hosts' Matty Cohen to send the Gingerbreads through to a third qualifying round tie at Solihull Moors.
Albans added: "There were some bizarre refereeing decisions to let Chasetown back in the game - the penalty shouldn't have been one and the sending off was doubtful.
"But we work very hard and if our tempo is right we're as good as anybody.
"Chasetown were at home and they're a good side. We knew they'd throw the kitchen sink at us and we rode our luck a little but I think it was a thoroughly deserved victory."