Bath boss Todd Blackadder admitted Saints gave his side 'a really tough game' at The Rec on Saturday.
Blackadder's men just edged over the line as Dan Biggar's late conversion hit the post to hand the home side a scrappy 17-15 success in torrid conditions.
Saints had gone 7-0 up after Cobus Reinach's try but Freddie Burns hit back after he intercepted Reinach's pass.
Bath then took the lead for the first time, taking a 17-7 advantage into the closing stages before Saints battled back to give themselves hope of a draw.
But Biggar couldn't make a difficult kick from the touchline as the home side celebrated a narrow victory.
And relieved Blackadder said: “It was a really tough game – you want to be the team that wins in conditions like that.
“I really felt at half-time that while we did not have a lot of territory, we were quite physically dominant. But a little lack of control and poor discipline let them back into it.
“We definitely had an edge in the scrums and in the second half our lineout went a lot better.
"Our line speed was good too, but there were little moments when we should have been more alive.”