The American striker provided a goal and an assist in an unlikely 4-3 win on Sunday (AEST), providing some light at the end of a very dark tunnel for Schalke, which has endured a catastrophic season that has ended with the club being relegated for the first time in more than 30 years.
Frankfurt went into the game a point behind fourth-placed, aware it needed to win in order to keep hopes of UEFA Champions League qualification alive, and in a position to put pressure on Dortmund ahead of its game at Mainz on Monday (AEST).
Things didn't pan out quite as planned initially, as Tuta tripped Amine Harit in the penalty area inside the first 15 minutes, giving the home side a penalty.
Klaas-Jan Huntelaar's spot-kick was saved by Kevin Trapp, but the veteran Dutch forward reacted quickest to the rebound to prod home the opener.
The Royal Blues have the worst defensive record in the Bundesliga by quite some margin this term, however, so Frankfurt was always going to get chances – and it converted its first real opening when Amin Younes's left-wing cross deceived goalkeeper Ralf Fährmann, allowing Silva to head in at the back post.
Schalke coach Dimitrios Grammozis brought on Hoppe at half-time to give his side fresh inspiration going forward, but it was the away side that looked more dangerous to start with.
Timothy Chandler headed just wide of the post from a trademark teasing Filip Kostic cross, before the Eagles took the lead via Evan N'Dicka, who headed in his third goal of the season from Daichi Kamada's corner.
The hosts hit back almost instantly, though, Huntelaar's deft back-heeled flick setting academy graduate Blendi Idrizi through on goal to fire Schalke level.
That kick-started a goal frenzy from the home side, with Hoppe setting up Florian Flick to fire the Bundesliga's bottom club ahead again, before the American striker got on the scoresheet himself, dribbling from the halfway line before coolly curling past Trapp and into the far corner.
Silva reduced the deficit in the closing stages with his 27th goal of the season – a new club record – but Frankfurt was unable find the net again, the loss doing serious damage to its chances of leap-frogging Dortmund into fourth with just one round of fixtures remaining.