Red Roses full-back Kildunne was making her 50th appearance for Quins, but it was Saracens who made all the early running at the StoneX Stadium.
Corrigan opened the scoring in only the second minute and the visitors were already trailing 19-0 when Katie Shillaker scored out wide to put Quins on the board.
Poppy Cleall was sin-binned for the home side in the 28th minute but they extended their advantage before the break with a debut try from Laets Royer.
Sydney Gregson put Corrigan in for her second try of the game at the start of the second half but while Kildunne touched down for Quins to make it 33-10 with seven minutes remaining, Louise McMillan and Amelia MacDougall countered with two late tries for Sarries.
Bristol Bears opened their campaign with a 12-try rout at Leicester Tigers in what was Scott Lawson’s first game in charge of last season’s fourth-placed finishers.
Millie David led the charge with an impressive four tries, followed closely by a hat-trick from speedy winger Reneeq Bonner at Mattioli Woods Welford Road.
Ella Lovibond weighed in with a couple, while there was also a try apiece for Bristol’s Evie Gallagher, Amy Dale and Holly Phillips.
The only sour note for the Bears was an injury to centre Phoebe Miller, who left the ground on crutches after being forced off midway through the first half.
World Cup winner Holly Aitchison could not inspire Sale Sharks to a second victory in as many games after returning to the squad for her first match of the season at Loughbrough Lightning.
The home side, which included Red Roses duo Sadia Kabeya and Lilli Ives Campion, bounced back from their narrow opening-day defeat at Harlequins to record a 19-12 win at Franklin’s Gardens.
Tahlia Brody gave Lightning a first-half lead with a try on her debut, while Haineala Lutui touched down twice in the second half.
Tries for Sharifa Kasolo and Rhona Loyd secured a losing bonus point for Sale.
