The British Lions wing showed why he is still one of the most feared attackers in the northern hemisphere, by dancing past three Llanelli defenders on the way to his 72nd minute try.
Sale deserved their win over a Scarlets side who struggled after head coach Phil Davies rested his Wales stars ahead of Saturday's crunch Heineken Cup clash with Toulouse.
Robinson's try left Sale director of rugby Phillipp Saint-Andre describing his as a 'born winner', but Davies was making no excuses as his side bowed out of the Anglo-Welsh cup.
Llanelli missed their first-choice players and centre Matthew Watkins was ruled out just before kick off after tweaking his back. It was mainly a second-string Scarlets side with Wales flanker Dafydd Jones making his first start of the season after shoulder surgery in the summer and Scottish lock Scott McLeod back from October's knee injury.
In contrast, Sale have had a nightmare on the injury front with key forwards Andrew Sheridan and Jason White out for the rest of the season. The loss of chief playmaker and England No.10 Hodgson has been their biggest blow. His reliable kicking was sorely missed, but when Frenchman Daniel Larrechea was relieved of the kicking duties after missing his first four kicks, former Cardiff Blues centre Lee Thomas stepped into the breach.
Behind Sale's robust pack, scrum half Sililo Martens and Larrechea ran the show, bringing a stream of runners onto the ball at pace, forcing Llanelli on the back foot.
Referee Rob Debney sent Scarlets prop Iestyn Thomas to the sin bin after 11 minutes for a professional foul and in his absence, Martens found enough space on the blindside from the base of the scrum to dart over. The try went unconverted, but Llanelli launched their first sustained attack and pounded the Sale line.
Under the pressure, Sharks prop Stuart Turner earned a yellow card for killing the ball and the Scarlets took full advantage. Lock Vernon Cooper took clean line-out ball and his pack marched over the line for Thomas to make amends for his earlier yellow card to claim the unconverted try.
Sale hit back immediately and Thomas banged over a penalty on the half-time whistle to give the hosts an 8-5 lead at the break. He put Sale in the driving seat with two well-taken penalties which gave them a nine-point cushion with ten minutes to go before Robinson worked his magic out wide and took the Sharks into the semi-finals.
Sale: Martens, Robinson tries, Thomas con. Thomas (3) pens
Llanelli Scarlets: Iestyn Thomas try