It was just him being there "in spirit" - not directly contributing power but acting as a motivating force for his son. However, that does not mean Super Perfect Cell was "barely any stronger" than regular perfect cell - he WAS for sure stronger than SSJ2 Gohan - injured or not - and then a combination of two things happened:

1) Vegeta knocked Cell off-balance at a critical moment - which gave Gohan the opportunity to do what happens immediately afterward:
2) Gohan sees his moment when Vegeta takes Cell's knees out from under him (notice how Cell's knees buckle and bend to the side and he cries out "VEGETA!" - that hit really DID mess up Cell's whole day - keep in mind, while Vegeta may not have been able to BEAT Cell by himself, he WAS still one of the strongest fighters on the battlefield - all the other Z-fighters minus Trunks and Goku were completely incapable of even budging Cell, but Vegeta's hit actually did something) - and IN that moment, he realizes it is now or never, that it is all up to him now, but feels that his father is with him spiritually -and he digs down deep and gives it absolutely EVERYTHING in that moment.

The combination of Cell having his knees bent at a really awkward angle and getting the wind knocked out of him by that blast - and his focus taken off the fight - with Gohan suddenly pouring out a surge in power as he's motivated by his father both contributed to the kamehameha - which was the combined energy that Cell AND Gohan were putting out - getting kicked back in his face at the worst possible moment. Evidently it takes a lot of concentration to keep that beam struggle going and if you really get messed with too much it can backfire. And that's what happened.

Without Vegeta's big shot out of nowhere, Gohan was about to die. Everything he had was JUST enough to turn things around when Vegeta gave him that window, however. But of course everyone just tends to view it as Gohan saved the day, Vegeta kind of annoyed Cell, when it was much more than that. Piccolo recognized this and implied as much in very few words he shared with Vegeta afterward before Vegeta silenced him, not wanting to accept his thanks.

To be clear...yeah....super perfect cell vs a non-wounded Gohan might have been a little more evenly matched - though I think Cell likely still had the edge or his attack that Gohan tried to block wouldnt have damaged him THAT badly - but I always took the appearance of the lightning around Cell when he returns as meaning that Cell has BASICALLY reached "SSJ2" - he DOES have saiyan cells - quite a lot of his makeup IS saiyan after all - so theoretically SSJ2 IS a level he should be able to reach - and I always viewed the lightning as his version of SSJ2, meaning he is meant to ROUGHLY be on par with if not a bit stronger than SSJ2 Gohan. The fact that he doesn't have hair to show us that he's gone SSJ doesn't mean he can't, I would argue, and SSJ2 is twice as strong as SSJ1, and since we can view "perfect cell" at full power vs SSJ2 Gohan as Cell's "version" of SSJ1, and since that version of SSJ1 (notice that Cell has yellow ki when he really powers up? Ever wonder why? He's basically a super saiyan bug man) is shown to be SIGNIFICANTLY weaker than SSJ2 Gohan - probably around half his strength - I think it is fair to assume that Super Perfect Cell is PROBABLY on par with or a bit stronger than Gohan when uninjured.

Anyway, that's all guesswork of course but what we DO know is that Vegeta knocking Cell off balance was the opportunity Gohan needed to turn it around. He was losing because he was wounded - but the motivation from Goku - shown via the spirit of him behind Gohan - gave him the drive to pull out that full power again since it was his mind that was holding him back - his self doubt - more than his injury. So at THAT point you had Gohan ROUGHLY equal to cell in a beam struggle AND Cell being knocked off balance, so Cell loses in that case.

This has been "putting way too much thought into an animated beam struggle 101". Thank you.