In the Buddies' three previous attempts to overturn Kilmarnock this term, the best they had managed was two draws, but they finally overcame Kenny Shiels' side with McGowan's spot-kick success 15 minutes from time ahead of a late Newton effort.
John McGinn had put Danny Lennon's side ahead with his first senior goal after 20 minutes but Kris Boyd levelled soon after for the hosts. Killie's unbeaten record against the men from Paisley was ruined, however, with McGowan and Newton's late intervention.
It was a Saints player who could be making his departure this summer, Kenny McLean - tipped for a close-season move to the npower Championship - who came up with the first effort on goal but his scissors kick from McGinn's corner was well off target on 16 minutes.
The supplier of that first chance made no mistake four minutes later, though, when presented with a more straight-forward attempt.
Newton drove to the by-line on the right before crossing to McGinn at the back post and the young midfielder did not even have to break stride to volley home with power from five yards out.
The visitors' lead lasted just five minutes as Borja Perez found a chink in the Buddies defence to play through Boyd, who stayed onside and poked the ball beyond the onrushing Samson.
Chances were more limited in the second half although Newton did see a deflected strike fly just over Cammy Bell's frame early on, while Boyd nodded wide from teenage winger Chris Johnston's corner after 73 minutes.
Within two minutes of that miss, though, Killie shot themselves in the foot. Lee Ashcroft slid in on another youngster, the Buddies substitute Anton Brady - also 19 - in the box when there was no immediate danger to concede a needless penalty, which was ruthlessly dispatched by McGowan.
With two minutes left, Newton signed off after a successful six-month spell in Scotland with just his second goal for the club, dancing past three half-hearted tackles before sliding the ball past Bell to wrap up the victory.