Bayern Munich were confirmed as German League champions last Sunday, but with two games left Schalke are almost certain to finish in the league's top three.
Asamoah's 34th minute header gave Schalke the lead before Croatian midfielder Ivan Rakitic put the result beyond doubt when he netted on 67 minutes and captain Marcelo Bordon added a late third with a header.
But rivals Werder Bremen have the chance to regain second in the league when they take on Hamburg in the north Germany derby on Wednesday night.
"We wanted to win our last three games to put Bremen under pressure. So three points were a must in Bochum," said caretaker manager Mike Bueskens.
"We are very pleased, but there is still plenty of football left this season."
Hanover 96 keep alive their slim dream of a top five finish which will give them a place in Europe next season with a 3-0 win over Hansa Rostock on Tuesday.
Two second-half goals by midfielder Jan Rosenthal sealed the win that put Hansa Rostock bottom of the table and all but relegated after just one season in the Bundesliga.
Hansa are now five points away from safety and have just two more games to claw their way out of trouble.
VfB Stuttgart's chances of a Champions League place next season are all but over after their 3-2 defeat at Borussia Dortmund on Tuesday when Switzerland striker Alexander Frei hit two second-half goals.
With just two games left, the 2007 Bundesliga champions are six points off a Champions League berth.
Germany striker Mario Gomez - set to be one of the stars of next month's Euro 2008 - grabbed two second-half goals for Stuttgart, but it was not enough to prevent Dortmund taking the three points.
Frei put his side ahead on 59 minutes with a direct free-kick and then made the result safe by slotting home a cross on 78 minutes which proved to be the winner.
Energie Cottbus picked up a valuable point with their 1-1 draw against Karlsruhe to leave them four points clear of the relegation zone.
On Wednesday night, champions Bayern take on Arminia Bielefeld at Munich's Allianz Arena determined to add to their nine-point lead at the top of the table.
"We have three games left, and we want to enjoy ourselves for the rest of the season," said Franck Ribery.
The French midfielder is set to return along with Lucio, Zé Roberto and captain Oliver Kahn, after the quartet missed out on Sunday's trip to Wolfsburg where a 0-0 draw confirmed Bayern as champions.
Also on Wednesday, Bayer Leverkusen who are just outside the top five and are desperately chasing a place in Europe next season host Hertha Berlin.
And mid-table sides Eintracht Frankfurt and VfL Wolfsburg will battle it out.
There is also a relegation battle royal with bottom three sides Nuremberg and Duisburg both in desperate need of points.