Scrum-half Spencer kicked seven out of nine attempts at goal to win the man of the match award in a game dominated by place kicks. Sam Davies kicked three penalties of his own for Ospreys.
Wales centre Ashley Beck continued his comeback from hip surgery to make his first start of the season for the home side while fly-half Davies was the only member of the XV who started against Connacht in the Pro12 last week.
Aberavon centre Aled Jenkins, Neath prop Gareth Thomas, former Wales Under-20 lock Rory Thornton and Fijian back-rower Ifereimi Boladau all made their Ospreys debuts.
Saracens also paraded a number of their emerging stars with England Under-20 World Cup-winning captain Maro Itoje leading a youthful line-up that included five debutants.
It was something of a trip down memory lane for the Ospreys who last played a competitive game at the ground in Neath nine seasons ago.
The tactics of the match were dictated by a downpour just before the kick-off and after that any thoughts of running rugby were extinguished.
Sarries had much the better of the territory in the opening exchanges which was reflected in Spencer kicking penalties on six and 10 minutes.
Davies hit back with a 13th-minute penalty before Saracens suffered a setback when wing George Perkins was shown a yellow card for a dangerous challenge on Dafydd Howells who went up for a high ball.
And with the extra man Ospreys levelled matters at 6-6 with Davies’ second penalty on 22 minutes.
Saracens opened up another six point lead before the break with further penalties for Spencer on 30 and 34 minutes.
But Ospreys had the best try chance of the half. From a line-out the home side looked as if they were going to cross but flanker Lloyd Evans spilled the ball just short of the line.
The Ospreys did not help their cause three minutes into the second half when prop Gareth Thomas was sin-binned for a tip tackle on Matt Hankin.
But Davies struck first with his third penalty on 55 minutes before Saracens dominated most of the final quarter with Spencer kicking penalties on 57, 60 and 78 minutes.
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