The victory helped to keep the Bundesliga title race alive for at least a few more days.
Leon Goretzka got the ball rolling after 17 minutes before Klaas Jan Huntelaar converted a superb free-kick on 66 minutes to make it 2-0.
Eintracht Braunschweig pulled one back through Omar Elabdellaoui's deflected strike on 81 minutes but it was not enough to deny Schalke, who wrapped up the win with a stoppage-time third from Adam Szalai.
Schalke, along with second-placed Borussia Dortmund, needed victories on Saturday to ensure Bayern Munich could not win the title this weekend and the home side dominated from the off at the Veltins Arena.
Teenager Max Meyer forced a bright save from Daniel Davari in the first minute after the ball fell sweetly into the midfielder's path, courtesy of Huntelaar's face.
But Schalke's dominance would be converted into goals in the 17th minute when Meyer found Goretzka who charged forward and smashed home from 25 yards.
It was the 18-year-old's third league goal of the season following his summer transfer from Bochum.
Davari's job in the Braunschweig goal was difficult enough, but some poor defending in the first half made his life harder.
Meyer tested the Iran international on 23 minutes, while Huntelaar was denied by a good save from the keeper 10 minutes later.
But the former Real Madrid striker would find his rhythm on 66 minutes, smashing home a 25-yard free-kick into the top corner, leaving the Braunschweig keeper helpless.
Eintracht were restricted to just a couple of challenging attacking moves throughout the 90 minutes with the hero of recent months, Ralf Fahrmann, tipping over from Dominick Kumbela with 15 minutes left.
The Royal Blues suffered a scare when Elabdalloaui's shot rolled past Fahrmann with eight minutes to play to make it 2-1, but Szalai's third late on secured the points for Jens Keller's side.