Opposition view: Bath boss Blackadder admits Saints were a tough opponent
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.
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Hide AdBath 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.”