A late goal from Liam Hook five minutes sealed the win for the Cuckoos who were 1-0 down at the break. On-loan Posh youngster Hameed Ishola equalised in the opening minute of the second-half before Matt Sparrow gave Yaxley a 53rd minute lead.
Lowestoft levelled with an 83rd-minute penalty, but Hook struck two minutes later to send Yaxley into tomorrow’s fourth qualifying round draw.
They will be joined by Peterborough Sports who also won a five-goal thriller at fellow Southern League Premier Division Central side Hednesford.
It looked plain sailing for Sports after goals from Jordan Nicholson and Mark Jones gave them a 2-0 half-time lead, but the hosts were back on terms with 15 minutes to go thanks to two penalties.
But Jones nodded in a 79th minute winner.
Spalding boss Gaby Zakuani was delighted with his side’s effort against higher-level Tamworth, but the Tulips bowed out 4-2 on penalties after a late Stefan Broccoli goal had forced a 1-1 draw. Former Posh youngster Shaq McDonald had given Tamworth the lead.
Wisbech boss Brett Whaley was less pleased with his side’s display as they went down to two second-half goal to Biggleswade even though the visitors play a division above the Fenmen.