Southampton started the encounter as the brighter side and broke the deadlock after 30 minutes through Lambert. The striker, who had been nursing a hip injury, saw his effort beat Matt Gilks via a deflection off Blackpool defender Craig Cathcart.
Both sides had chances to take the lead going into the break but Lambert saw a powerful effort saved by Gilks, while up the other end Matt Phillips struck the post for Blackpool.
League leaders Southampton asserted a large amount of pressure on the visitors and it finally told three minutes into time added on.
Frazer Richardson was the creator, crossing in for an unmarked Lambert to head past Gilks.
Southampton are now three points clear at the top of the Championship table.