Victory ended the hosts' own poor run of four consecutive losses and moves them up to sixth in the table.
Ben Foden and Tom Wood's tries gave Saints a deserved 14-0 half-time lead.
Sale's rugby league convert Denny Solomona marked his Premiership debut with a superb, acrobatic finish before Luther Burrell's late Northampton try.
Victory came at the end of a tough week on and off the field for Saints, who avoided any sanctions when a lengthy review into wing George North's latest head injury was published on Wednesday.
They were thrashed 60-13 by Leinster in the Champions Cup last Saturday but Foden's early try quickly lifted the mood for Jim Mallinder's side.
Stephen Myler was clinical with his boot, converting all three Saints tries and adding a precise, second-half penalty.
Sale, who have not won in the league since October, improved in the second half after Mike Phillips was sent to the sin-bin and Solomona's brilliant try got them on the scoreboard, diving over the Saints defence when just inches from the touchline.
For the hosts, Louis Picamoles was outstanding, while the impressive Nic Groom had two tries correctly ruled out; one was for a narrowly forward pass and another for letting the ball slip fractionally out of his grasp on the try line.
Northampton director of rugby Jim Mallinder:
"We started well for a change and attacked with accuracy.
"It's disappointing we didn't get a bonus point as we needed Nic Groom to score one of the two tries that were disallowed by the TMO.
"We've got Gloucester next week and then Bristol at home. These are games we are capable of winning and if we do we can move up the table."
Sale Sharks boss Steve Diamond:
"We are not clicking at the moment as we are panicking under pressure and can't beat anyone at present.
"We've got to keep plugging away but our recruitment is in place for next season when we will have four or five new players.
"We need leaders and direction and hopefully the new recruits will provide this. With 20 minutes to go, I thought we had a real chance of getting a bonus point but we couldn't convert our chances."
Northampton Saints: Foden, Pisi, Burrell, Hanrahan, Estelles, Myler, Groom, Waller, Haywood, Brookes, Lawes, Day, Wood (capt), Harrison, Picamoles.
Replacements: Clare, Waller, Hill, Ratuniyarawa, Gibson, Kessell, Wilson, Tuitavake.
Sale Sharks: Haley, Solomona, James, Leota, Charnley, MacGinty, Phillips, Harrison, Webber, Aulika, Evans, Ostrikov, Neild, Lund (capt), Ioane.
Replacements: Briggs, Flynn, Longbottom, Mills, Beaumont, Seymour, Mitchell, Arscott.
Northampton Saints earned a much-needed Premiership win at Franklin's Gardens to inflict a seventh straight defeat in all competitions on struggling Sale.