Bath had regained top spot by beating local rivals Gloucester 30-26 on Friday, but Saints made sure their stay was brief.
Phil Dowson's men outscored their hosts by seven tries to four, touching down through Tommy Freeman, Rory Hutchinson, Robbie Smith, Edoardo Todaro, Josh Kemeny, Alex Coles and Henry Pollock.
Victory means the 2024 champions have 43 points after 10 games -- two clear of second-placed Bath.
Sale, who suffered a club-record 77-7 defeat at Toulouse last week in the Champions Cup, showed impressive resilience to fight back after going 14-0 down early on.
But Northampton showed their mettle to win at Sale for the first time since 2017.
"Sale are a very good side, so we knew it was going to be nip and tuck, and it was a mad game with the wind, which made it pretty chaotic," said Northampton director of rugby Dowson.
"I thought we stuck to our guns enough to get the win in the last 10 minutes."
Third-placed Bristol edged a war of attrition at Exeter 8-3 while Leicester beat Harlequins 34-7.
Saracens ended a turbulent week by overwhelming Newcastle, with Noah Caluori taking star billing at Stone X Stadium.
The day after Saracens announced director of rugby Mark McCall would be stepping down after 15 seasons in charge, they scored 11 tries against the Prem's bottom-placed side.
It was a much-needed tonic after last week's crushing 28-3 defeat by Glasgow, the most recent setback in a disappointing season in which consistency has proved elusive domestically and in Europe.
"Today was an important day because those five points keep us close enough to the mix," said McCall. "There are eight games left, so there's everything left to play for."
He added his decision to step down at the end of the season was a "big weight off my shoulders".
"I've been sitting on it for a while, and now that everybody knows, I feel a bit lighter," he said.