Hodgson and Jones traded two kicks each in an uneventful opening half but Worcester took charge of the match when flanker Talei crossed at the start of the second period.
Worcester piled forward and from a scrum near the Sale line, the ball was spread wide and Talei collected it at pace to barge his way over.
Jones, who had missed a penalty in the first half, failed to claim the conversion and Sale were back in the hunt with Hodgson's penalty on 55 minutes.
Sale, who were without Kiwi centre Luke McAlister because of a hamstring strain, could not find a way through the Worcester defence but the visitors were profligate with the boot - Chris Pennell and Jones missing two more penalties.
But Jones managed to find his range and an important time and two penalties saw his side home.
Sale rugby director Philippe Saint-Andre on a possible injury scare for Mathew Tait:
"Tait's hamstring went tight and because he had pulled it before we didn't want to take any risks and so brought him off.
"We don't know how serious it is."
Saint-Andre on the result:
"Worcester deserved to win and this was one of Sale Sharks' worst performances since I've been involved in the club.
"I take a lot of responsibility for this and I'm very, very concerned.
"It's the first time in my coaching career of 11 years that I've lost four home games in succession.
"We're missing a lot of players through injury and international call-ups and we've got to try and get ready for Wasps next weekend. We have eight days to improve."
Worcester boss Mike Ruddock:
"It was a very good performance - we played well and deserved our win.
"At 6-6 at half-time, I thought we had probably had had the better of the half but hadn't manage to penetrate.
"I asked the boys to carry on playing that way because I felt we would get an opportunity and that's what happened as we scored a great try."
Sale: M Tait; Cueto, Keil, Bell, Doherty; Hodgson, Wigglesworth; O'Donnell, Briggs, Turner, Schofield, Cockbain, Ormsby, Abraham, Fearns. Replacements: McLeod for M Tait (72), Tuilagi for Keil (53), Gaskell for Cockbain (68), D Tait for Ormsby (11).
Not Used: M. Jones, Davies, Leck.
Worcester: Latham; Pennell, Rasmussen, Tuitupou, Benjamin; M Jones, R Powell; Mullan, Fortey, Tuamoepeau, Rawlinson, Gillies, Talei, Sanderson, Horstmann. Replacements: Crichton for Tuitupou (76), M Powell for R Powell (49).
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