Last season's runners-up needed the skills of Marco Reus, who this week extended his contract with the club until 2019, as the German international scored one goal and set up another to lift them into 14th spot with 22 points.
The visitors shocked Dortmund in the first minute when keeper Roman Weidenfeller failed to clear after a mistake and Elkin Soto lobbed the ball into an empty net from the edge of the box.
"Their lead was slapstick. Terrible goal," Dortmund coach Juergen Klopp told reporters. "We were unlucky to hit the post but we knew we would get our chances if we kept up the pressure.
"If we stay compact we are brutally strong. Then we scored the goals and everything was fine."
Dortmund, despite having their backs to the wall after a dismal first half of the campaign, kept their cool and Reus almost equalised a minute later in a furious start to the game as his powerful shot rattled the woodwork.
Mainz's reserve keeper Stefanos Kapino, making his first Bundesliga start, then did well to deny Pierre-Emerick Aubameyang.
Dortmund finally struck five minutes after the restart as Neven Subotic beat his marker to head in a corner and spark wild celebrations among the home fans who had whistled the team off at halftime.
The hosts, who take on Juventus in the Champions League last 16 later this month, then turned the game around with Reus charging through to beat Kapino after Kevin Kampl's fine assist.
Mainz, who are 13th, bounced back as Lebanese Yunus Malli beat Weidenfeller, who has struggled this season and briefly lost his place, to equalise in the 56th minute and again stun the 80,000 crowd.
Reus, though, came to the rescue for Dortmund by delivering a superb curling pass with the outside of his boot to beat the offside trap and send Aubameyang through to make it 3-2 in the 71st minute.
Nuri Sahin's 78th-minute goal sealed Dortmund's second consecutive victory in the league and hauled them out of the relegation zone for the first time since early December.
On Saturday, leaders Bayern Munich will try to protect their eight-point advantage against Hamburg SV while second-placed VfL Wolfsburg take on Bayer Leverkusen.
(Reporting by Karolos Grohmann, editing by Tony Jimenez)
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