With the Europa League and DFB-Pokal also on the agenda, Hyypia wants his side to build up a head of steam with no more breaks between now and the winter recess on December 19.
Leverkusen could potentially have 16 games to fit in to those eight and a half weeks, and it could well be a very fruitful two months if all goes according to plan.
"We want to put together a good streak up until Christmas to edge up towards the top positions," said Hyypia.
"A win over Mainz could start us off in the right direction and that has to be our goal."
In truth, Leverkusen have already started a streak of sorts with seven points from their last three matches, making the international break more of an inconvenience than a welcome chance to rest, although it has given Lars Bender time to recover from a knee injury.
"Things are looking good with him at the moment," Hyypia told reporters at a press conference.
Sidney Sam has not been able to recover from a niggling muscular strain, though, and Renato Augusto will also miss out.
Mainz also found their form just before the international break with back-to-back wins lifting them away from the danger area.
However, their coach Thomas Tuchel does not believe the intervening time will have eroded his side's confidence levels.
"We do have self-confidence, and it has grown," he said.
"Hopefully we will see that tomorrow [Saturday] in the way we play."
A goal on international duty for Adam Szalai and qualification for the European Under-21 Championship for Germany international Jan Kirchhoff means their spirits will be high anyway, although they need to bring that with them into their club football, says Tuchel.
"They need to be with us both in body and in spirit," he said.