Bourne Town shared six goals with Whitworth – but came so close to victory.
The Wakes went ahead through Scott Dore after two minutes and he made it 2-2 just before the half-hour mark.
Jack Humphries put Bourne ahead with seven minutes left but Dore was dismissed for a second bookable offence and the Wellingborough side levelled six minutes into stoppage-time at Abbey Lawn.
Boss Jimmy McDonnell said: “The lads performed well with an honest effort as a team.
“We had the disappointment of losing 5-1 at home in the cup last Tuesday night. All the best to Ketton - they were the better side on the night but we weren’t at it.
“We had good numbers at training on Thursday and changed a few things for Saturday’s game.
“We went to four at the back to provide more protection and Max Cooper moved to left-back to nullify their pace down that side.
“Scott, who has moved to the area, is a hard-working lad who finished well for the first goal.
“Whitworth have got a little bit of quality which showed with their two goals and we could have easily thrown in the towel.
“But we reacted well and got ourselves back in front. At 3-2 we had a great chance to seal the win.
“We were told there would be two minutes added on then Scott was sent off, they missed a chance and scored in the 96th minute.
“The lads were disappointed being so close but they came up against a very good side.
“Going forward, we played good football but we can’t keep clean sheets so we need to out-score teams if we can.
“The performance was full of positives and there is no great shame in that result.
“We had a good crowd again and the message is getting out there that Bourne will give a chance to young lads.”
On Saturday, Bourne will have more support for the trip to Thrapston Town.
McDonnell added: “We had an idea of running a bus and it should be a good day out for everyone.
“Hopefully, other clubs in the division will return the favour in the future as we don’t normally see many away fans.”