The former Stuttgart striker sealed Leipzig’s win in the 74th and claimed his second goal in the 88th off an assist from Poulsen, who grabbed two goals in five minutes in the first half.
Karim Onisiwo pulled one back before the break for Mainz, which remained 10th.
Frankfurt, which has been impressing with its performances in the Europa League, bounced back from two successive defeats in the Bundesliga with a 2-1 win over Bayer Leverkusen to stay in pursuit of Leipzig in the race for Champions League qualification.
Filip Kostic set up Danny da Costa to score against his former side in the first half, then grabbed Frankfurt’s second before the hour-mark.
Karim Bellarabi gave Leverkusen hope in the 65th, but Kevin Volland missed a good chance for an equalizer in injury time.
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