Hyypia's men sit fourth in the Bundesliga - which would be good enough for a place in next season's Champions League preliminaries. But they must turn around a wretched recent record at the BayArena if they are to climb any higher.
Bayer have lost all of their last five home games in all competitions, but this weekend face the team with the worst away record in the division. Eintracht Braunschweig are bottom and have won just one league game away from home this season.
Hyypia hopes that the win at Augsburg last time out was just the start.
"We have recently been told that we had nine finals. The first we lost, and we won the second. Now there are seven. If we fight, run and defend as we did in Augsburg, we have good chances to win," the Finn told the club's official website.
"We certainly did not play great football against Augsburg but the guys showed fight and had the right attitude. This is the prerequisite to win games and to have success."
Stefan Reinartz's persistent heel problems mean he joins Robbie Kruse and Jens Hegeler on the Bayer injured list, but midfielder Sidney Sam could be back after missing the Augsburg match with a knee injury.
Braunschweig are bottom but by no means cut adrift, and were victorious over Mainz last time out to leave them five points behind a place of complete safety, and three behind Hamburg in the relegation play-off berth.
Braunschweig coach Torsten Lieberknecht told his club's official website: "The development of the team is crucial to be able to say that we can still gather points and achieve the great goal of avoiding relegation. A point helps but a victory against Bayer would be even more advantageous. We of course will strive for the maximum."
Lieberknecht warned his players not to lose composure even if they find themselves out of possession for long periods of the game, as was the case when they beat Leverkusen at home in November.
"A game can be won with one or two chances - even with 18 per cent of possession. In addition, aggression and combat readiness must be kept high," he said.
Ermin Bicakcic is set to miss out with a hand fracture, and fellow defender Marcel Correia has a muscular problem. Long-term absentees Marc Pfitzner and Karim Bellarabi are still missing.