The Scarlets swept into a 14-3 lead thanks to tries by Andy Fenby and Gareth Davies, both of which were converted by Owen Williams.
Cipriani's boot edged Sale closer with two penalties before Richie Vernon drove over from close range while Jake Ball was in the sin bin.
Charlie Amesbury went over for a converted try on the stroke of half-time after the ball was spun quickly through the hands of the back division from right to left, leaving the Scarlets defense running out of numbers and allowing Amesbury to dive over in the corner for a try converted by Cipriani.
Williams and Cipriani traded penalties in the opening 15 minutes of the second-half, but the Sale fly half was off target with another attempt after Rhodri Jones had been binned for not rolling away.
Cipriani was in no mood to loosen the thumb screws and sped over next to the posts to convert his own try as the Scarlets were made to pay for their indiscipline.
Charlie Ingall powered over from close range to touch down for his side's fourth try to send the Sharks to the top of Pool 2.