When Cueto (left) went over it gave Sale much-needed breathing space
Sale took a massive stride towards Guinness Premiership safety and pushed Worcester closer to the drop as they outplayed the Warriors at Edgeley Park.
Two drop-goals and a penalty from Charlie Hodgson, to a Willie Walker penalty, gave Sale a 9-3 half-time lead on Friday night.
Hodgson added a second penalty before Mark Cueto crossed in the corner to send Sale well clear.
The Sharks now have 31 points, six clear of bottom-placed Worcester.
Perennial strugglers Worcester have much more experience of relegation battles than their hosts, who were champions back in 2006.
But although the visitors enjoyed plenty of possession, especially in the first half, they lacked the cutting edge to break down Sale's rock solid defence and in the end the hosts' superior class told.
England centre Mathew Tait was a constant presence in both attack and defence and winger Cueto enjoyed a feisty night's work, while half-backs Hodgson and Richard Wigglesworth also impressed as Sale secured their sixth league win of the season.
Hodgson missed a ninth-minute penalty for the hosts before, after a concerted spell of Worcester pressure, Chris Pennell and Willie Walker were both off target for the visitors.
Sale were under the cosh in the early stages but they tackled like tigers and when they finally established a bridgehead in Worcester territory, Hodgson broke the deadlock with a simple penalty.
Tait was then heavily involved in a sweeping Sharks attack and Hodgson popped over a short-range drop-goal to double the hosts' advantage as typically insistent Mancunian rain began to fall.
Walker missed a second kickable penalty just before the break and they trailed 9-0 at the interval after Hodgson landed a snap drop-goal as Sale gave the visitors an object lesson in taking their chances.
The visitors finally got on the scoreboard when Tait was penalised for a shocking tackle on Walker, who picked himself up to drill the ball between the posts.
Hodgson missed a chance to restore the nine-point margin when he pushed a penalty wide but he made no mistake when Worcester replacement Chris Cracknell lost his head and picked the ball out of a ruck in the 22.
Then came the clinching moment, as the incisive Tait made a half break and, after Neil Briggs and Marika Vakacegu took the ball on, Cueto crossed in the corner for his first try of 2010.
Hodgson could not convert but despite Worcester launching some desperate late attacks and coming within inches of scoring through Cracknell, Sale were well worth a vital victory.
Worcester director of rugby Mike Ruddock told BBC Hereford and Worcester: "We had a try-scoring chance in the second half and we felt we had got that over the line and scored but the video replay was inconclusive.
"I looked at it and thought it was definitely a try and Chris Cracknell thought he had scored, but it wasn't given and in the end it wouldn't have been enough to win the game.
"I am proud of my players as we shoved in a big effort, tried our best and worked to the last minute.
"At the end of the day we weren't quite good enough and Sale edged it."
Sale: Vakacegu; Cueto, M Tait, Thomas, Cohen; Hodgson, Wigglesworth; E Roberts, Briggs, Forster, C Jones, Schofield, Koyamailbole, Seymour, Ormsby.
Replacements: M Jones for Briggs (63).
Not Used: Schwalger, Kerr, O'Donnell, Cox, Leck, Kennedy, James.
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