Havertz goal breathes life into Leverkusen's campaign
Havertz, 19, who made his Germany debut in the 2-1 friendly win against Peru earlier this month, claimed his first Bundesliga goal of the season with a powerful header midway through the second half.
After losing their first three games of 2018/19, Leverkusen climbed up to 15th, leaving bottom side Schalke, who were beaten 2-0 at home by league leaders Bayern Munich on Saturday, as the only team in Germany's top flight to have lost all four games this season.
However, Leverkusen made hard work of the win at their own BayArena.
Only an intervention by the video assistant referee denied Mainz the opening goal just after the break when their Sweden striker Robin Quaison, who had just come on, headed the ball into the net, but replays showed the ball clipped his hand in the build-up.
After the let off, Leverkusen took their chance to claim their first win of the season when Havertz headed home a cross from his Germany team-mate Julian Brandt on 62 minutes.
Ridle Baku, 20, fired wide with a late chance for Mainz, who suffered their first defeat of the season to drop to seventh.