Hyypia's men came from behind to take all three points against Thomas Schneider's side, Eren Derdiyok scoring the winner six minutes from time after Stefan Kiessling had cancelled out Moritz Leitner's opener.
The win ended a streak of three consecutive Bundesliga defeats for second-placed Leverkusen, and Hyypia was quick to praise his players for showing better balance, which he believes should inspire confidence among them.
"We didn't start the game so well and conceded very early on," Hyypia said.
"We had talked about wanting to set the game at a very high pace because Stuttgart had to play a difficult game against Bayern midweek and that would open up spaces towards the end when they got tired.
"But, that didn't work. We just didn't play well in the beginning. Obviously after 1-1 we had a few more chances to score more goals.
"During the week we also talked about the three losses. The games against Freiburg and then Bremen we wanted to win at all costs. Today we used our head a bit more. We kept a better balance.
"At 1-1 Stuttgart didn't have many chances to score and if we don't score another goal then it stays at 1-1 but today we got the second one.
"The players that scored today got vital goals for themselves too. Kiessling hadn't scored in a long time and Eren scored after a long goalless streak too so it was important for both.
"This win should give us confidence for the future and especially for Friday with our difficult game against (Borussia) Monchengladbach."
