Bundesliga leaders Bayern Munich started the weekend nine points clear after thrashing Wolfsburg 4-0 on Friday, but second-placed Borussia Dortmund can trim the gap when they face Hertha Berlin away later Saturday.
Frankfurt broke into the top five, having started last weekend 12th, as Lindstrom added to goals he scored in wins over Moenchengladbach and Leverkusen last week.
Japan veteran Makoto Hasebe snapped up a loose Mainz pass in the first half which resulted in Rafael Borre getting in behind the defence.
The Colombia striker chipped the on-rushing goalkeeper, straight into the path of Lindstrom who tapped in the winner on 35 minutes.
The clubs passed each other in the table as Mainz drop to eighth.