Mainz took full advantage of Borussia Dortmund's 1-1 draw with Hoffenheim earlier in the day to leapfrog them into top spot with 24 points, going two points clear after their eighth win in nine games.
Borussia Dortmund grabbed a deserved last-gasp equaliser with an Antonio da Silva free-kick to draw 1-1 with visitors Hoffenheim but the result ended their seven-game winning streak and left them second on 22 points.
Hoffenheim are fourth on 15, a point behind Hanover 96.
Mainz, enjoying an exceptional season in only their second successive season in the top flight, created their first chance when Hungarian Adam Szalai was left unmarked but failed to hit the target from inside the box.
Leverkusen, missing several key players through injury, could not match the pace of their visitors, who saw several of their efforts denied by keeper Rene Adler.
Ivanschitz, who had come on in the 69th minute, broke the hosts' resistance a minute later when Andre Schuerrle, who will join Leverkusen for 11 million euros next season, knocked the ball into space for the Austrian to tap it in from close range.
The hosts, who drop to fifth on 15 points, fought back in the remaining 20 minutes and hit the crossbar through Sidney Sam late in the game but failed to find the equaliser.
BORUSSIA GOAL
Borussia looked to be heading for a first loss since August when Demba Ba fired the visitors ahead in the first half but Brazilian Da Silva curled in a free-kick with the final kick of the game.
"This is a huge relief," said Dortmund coach Jurgen Klopp. "Our performance in the second half was unbelievable."
Hoffenheim took an early lead through Senegalese striker Ba, who tapped in his fifth goal of the season from two metres after a pinpoint cross from Luiz Gustavo in the ninth minute.
Borussia reacted instantly and were awarded a penalty for an Isaac Vorsah handball on 15 minutes.
Turkey international Nuri Sahin converted from the spot before the referee ordered him to retake it. His second attempt was saved by keeper Tom Starke.
Dortmund continued to dominate but had to wait until the third minute of stoppage time to level.
With defeat only seconds away, Dortmund were awarded a free-kick just outside the box on the right with substitute Da Silva stepping up to score before Hoffenheim's Sejad Salihovic was red carded for complaining to the referee.
Schalke 04's poor start to the season continued on Saturday when last season's runners-up drew 0-0 at Eintracht Frankfurt to stay near the relegation zone with six points.
Fellow Champions League competitors Werder Bremen crushed hosts Borussia Moenchengladbach 4-1 to move up to eighth in the table on 14 points.
Bayern Munich escaped with a 0-0 draw at Hamburg SV on Friday to remain in 11th place on 12 points.
