Sale applied early pressure and they were rewarded in the fifth minute when a well-weighted kick by fly-half Mike Hercus – who had missed two earlier penalty attempts – found Jason Robinson waiting out wide to scoop the ball up and score.
But Hercus' boot failed the Sharks once again when his conversion attempt sailed wide of the posts.
The Tigers, meanwhile, were denied a try by the television match official and their troubles were compounded further when a loose pass by flanker Will Skinner was snaffled up by Sale No.9 Bryan Redpath who darted over for another Sale try.
Hercus continued to miss the mark, however, and he sent another penalty attempt wide not long after.
And the USA Eagles star's afternoon got worse when he hit the posts with an attempted drop-goal and the Tigers snaffled the ball up to take play into Sale territory for centre Daryl Gibson to go over for their sole try of the game.
Goode made no mistake with the conversion attempt and the Sharks – who could have been comfortably in front – led by just three points. Minutes later Goode leveled the scores with a drop-goal.
But Hercus saved face slightly when he put Steve Hanley through the gap with a back-pass and Hanley sent winger Mark Cueto over for his team's third try. Hercus finally found his range and extended the lead further.
The second half saw the arrival of Charlie Hodgson with the England star replacing Hercus at No.10, but it was the Tigers who were on the board first when Goode put over his second drop-goal of the game.
Goode closed the gap further with a penalty, while the Sharks fans nervously looked on as Hodgson sent an attempted drop wide of the posts. Goode gave the Tigers the lead for the first time in the match with another penalty.
Hodgson then had another drop-goal attempt disallowed for an earlier knock-on, but the England playmaker – who was restricted to a 40-minute appearance because of the 11-week recovery period for England internationals – reclaimed the lead with a succesful attempt soon after.
Hodgson extended the lead further with a penalty three minutes from time and then finally clinched victory for the Sharks with another during injury time.
For Sale:Tries: Robinson, Redpath, CuetoCons: HercusPens: Hodgson 2DG: Hodgson
For Leicester:Try: GibsonCon: GoodePens: Goode 2DGs: Goode 2