Back on the ice and looking to bring a veteran presence to a surprisingly successful New Jersey team, Boyle got on the board when he found the back of the net in his fifth game back on Thursday night.
But that goal would be the only tally of the first period for the Devils, who wasted some key opportunities while outshooting the Oilers, 12-7, over the first 20 minutes.
"I've never cried after a goal before", Boyle told MSG Networks during a first-intermission interview.
Boyle was diagnosed with chronic myeloid luekemia, a form of bone-marrow cancer, on September 19.
Anton Slepyshev and Milan Lucic also scored, and Cam Talbot made 32 saves for the Oilers (6-8-1), who have won two straight games for the first time this season.
The Oilers tied it early in the third period when Schneider got beat five-hole for a second time.
Drew Stafford, with his 10th goal in 19 career games against the Oilers, gave the Devils a 2-1 lead at 18:25 of the second period, faking a shot from the left before getting to the crease and pulling a shot around Talbot. "It's a tough league". You can't be interested in playing the right way.
Play evened out in the second period, where the Oilers tied it at 1-1. It's the Oilers' second-straight overtime win and their first set of back-to-back victories this season.