The black, green and gold, who had won 16-14 at Newcastle Falcons six days earlier, won a last-gasp breakdown penalty, as they had at Kingston Park, to put the seal on a 24-18 win against Bath.
Saints had moved into a nine-point lead when Fin Smith converted George Hendy's second-half try.
But Bath kept battling, sending on the likes of Alfie Barbeary and Ben Spencer as they mounted a late charge.
A Spencer penalty cut the gap to six points and Saints survived several scares before securing another precious four Gallagher Premiership points.
"We probably made it difficult for ourselves but we managed to pull through with some great defence," Dowson said.
"I thought we showed great character.
"I definitely thought we saw signs during the Premiership Rugby Cup in terms of the engagement with what we're trying to do (defensively).
"We've seen it in every game aside from the Bristol one where we went away from what we aspire to be.
"But last week and this week, the game comes down to the defence and that's credit to the players and (defence coach) Lee Radford.”
Saints also showed up at the scrum, winning several penalties against a strong Bath pack.
And Dowson said: "We were frustrated last week with the scrummaging performance but this week we've gone pretty hard at it.
"We were without Trevor Davison, who is unfortunately ill, but Paul Hill came in with a brilliant attitude and tremendous energy, which he always brings.
"I thought it was exactly the sort of statement Hilly would want to make in a game like this to show what he's about."