Bath boss Todd Blackadder was left to rue his side's failure to deal with the big pressure moment after Saints snatched victory at Franklin's Gardens on Saturday afternoon.
David Ribbans powered over after taking a quick tap penalty and James Grayson converted to put the seal on a dramatic 27-26 Gallagher Premiership victory.
Bath thought they had it won after Rhys Priestland landed two late penalties to take his tally to 16 points for the day.
But Ribbans added to earlier efforts from Rory Hutchinson and Alex Mitchell to make sure of four precious Premiership points, moving Saints up to fifth in the process.
"It's just pressure and it comes down to these moments," Blackadder said.
"We didn't exit, we could have, and probably should have to take that pressure off.
"There was a chargedown, penalties and on that last try one of the boys turned their back after all the work that was put in and that was the difference. Bang, it was gone.
"The game plan had been solid, defensively we had gone up a gear and our attack was some of the best we've had all season.
"It was a great game of rugby, we came here with a lot of self-belief and put everything into it but it was just that last minute that was the difference.
"The plan was to get up and put their skillsets under pressure, which we did for the most part, but we were a little bit eager in their 22.
"We went in ones but we should have gone in threes like they did in the end.
"We had a lot of opportunities out there, a good game plan, a good strategy and we played really well for 79 minutes."