Tries by Kameli Ratuvou and Joel Tomkins, to go alongside 10 points from the boot of Nils Mordt, gave Sarries a 20-12 half-time advantage at the Salford City Stadium, with Sale's response before the interval coming through Mark Cueto's score and a penalty try.
A Fraser McKenzie touchdown and a Danny Cipriani penalty took the Sharks into the lead before Ben Spencer's three-pointer edged the visitors ahead again, but Miller slotted a late penalty to earn the victory for the hosts.
With a vital Aviva Premiership encounter against Gloucester looming, Sale chose to select a weaker side to the one that had gone down 34-28 to London Irish the previous week.
However, it still looked stronger on paper than a Saracens team which rested the majority of their star players, particularly with Dwayne Peel and Cipriani starting at half-back for the hosts, and the seven-times capped England international showed his quality from the off when a superb cut-out pass put Corne Uys in space.
The centre then produced a similarly sublime piece of skill to send Cueto away in the corner unopposed. Jordan Davies missed the conversion, but the home side led 5-0 after three minutes.
That advantage did not last long, though, as two scores in as many minutes put the visitors in front.
Firstly, Mordt slotted away a penalty when Sale were penalised for holding on, before a length-of-the-field move ended in Ratuvou touching down.
Instigated by Nick Auterac, the prop showed impressive pace to run 40 metres. Excellent support work and good hands from forwards and backs alike put the Fijian in space, and he did the rest.
It seemed to unsettle the Manchester-based outfit and Ben Ransom almost extended the away team's lead, but his jinking run was halted metres from the line.
That missed opportunity was to prove costly as the Sharks proceeded to go up the other end and score when referee Llyr ApGeraint Roberts awarded a penalty try for collapsing a maul.
But Saracens always looked dangerous with ball in hand. Another Ransom break set up a penalty opportunity which Mordt duly converted to take it to 13-12 in the visitors' favour.
Sarries full-back Ransom then rounded off an outstanding individual performance in the first half as a third menacing run allowed Tomkins to cross the whitewash, with Mordt adding the extras from out wide.
As conditions worsened for the start of the second period, the match became scrappy, but Eoin Sheriff offered the hosts hope after he was sin-binned for repeated team infringements.
And Sale took advantage of the extra man as McKenzie evaded two weak tackles to go over, Davies converting.
Cipriani and Spencer then traded three-pointers as Sarries held a one-point lead going into the closing stages, before Miller's late effort from the tee gave the Sharks victory.
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