Former English and European champions Saracens, playing their first second-tier fixture following relegation for breaching the Premiership's salary cap rules, came off second best at the Mennaye Field in Penzance.
The visitors trailed 18-17 heading into the final four minutes and Pirates' replacement Rhodri Davies raced over for the match-sealing try.
Saracens, without England internationals Owen Farrell, Mako and Billy Vunipola, Jamie George, Maro Itoje and Elliot Daly, were quickly into their stride and wing Sean Maitland's unconverted try in the corner gave them the lead.
The Pirates hit back through stand-off Luke Scully's penalty and they went in front when skipper Tom Duncan barged over from a tap and go for their first try, which was not converted.
Sarries' lead was short-lived as the Pirates came storming back at the start of the second half, with hooker Dan Frost getting the final touch following a break down the blindside. Scully converted to put the home side 15-10 up.
The visitors responded in a see-saw battle and second row Tim Swinson muscled his way over for a converted try to edge them 17-15 ahead.
Scully's penalty after Sarries had infringed at a scrum hauled the Pirates 18-17 in front and when the visitors let the ball bounce from the home fly-half's big up-and-under, Davies pounced to collect and scamper over.