The West Country team had won three out of their first four games going into this encounter, but it was Sale who took a 16-10 lead into half-time.
They had traded tries through Andy Forsyth and Semesa Rokoduguni but it was the kicking of Cipriani which separated them in the opening period, converting three opportunities to George Ford's one.
The second period proved less eventful, with the stand-offs adding a three-pointer each as the Sharks held on for the win.
From the kick-off, the visitors looked to move the ball wide and test the home side's defence.
However, they were caught out when Stuart Hooper lost the ball on his own 22-metre line.
That allowed Steve Diamond's men to build their first attack of the evening and, when the Bath rearguard strayed offside, it gave Cipriani his first chance of points but his effort drifted wide.
It was not long before the seven-time England international opened the scoring, though, when he kicked a drop-goal after further Sharks pressure.
But Bath were soon into their stride. Gary Gold's team have looked to add a try-scoring edge to their game this season and they found a weakness on the hosts' short side which allowed Rokoduguni to scamper clear.
Instigated by veteran scrum-half Peter Stringer, the former Ireland international sucked in Dwayne Peel before sending the Fijian flyer clear. Ford converted and Bath led 7-3 with 11 minutes gone.
Alafoti Fa'osiliva, on for the injured Leroy Houston, then went close with his first touch of the match when he intercepted the ball from a loose Sale lineout.
However, after consultation with the television match official, the back-rower was ruled to be in touch.
That let-off seemed to spur the Sharks into action. Mark Easter, who was impressive in the opening half, broke the gainline and, from another Bath infringement, Cipriani added his second penalty from the tee.
It was the hosts who were now in the ascendancy with their driving game marching the visitors back with regularity.
Although the maul failed to produce a score, it sucked in their opponents' defence and they took advantage of the overlap outside to send Forsyth across the whitewash, Cipriani converting.
The respective fly-halves then traded penalties towards the end of the opening 40 minutes and the Sharks held a 16-10 advantage at the interval.
While the first period had plenty of excitement, the start of the second was dominated by Sale employing the choke-tackle to great effect and halting any Bath momentum.
And when that tactic resulted in a scrum, the visitors collapsed the set-piece and Cipriani was once again on target, this time from long range.
However, Ford reduced the deficit through a three-pointer of his own as the hosts went into the final quarter 19-13 ahead.
The away side were beginning to exert significant pressure on the Sharks' rearguard, and it eventually told as Michael Paterson was sin-binned.
But, despite Tom Biggs going close, Sale held firm to take the victory.