Leverkusen, who have now won four in a row in all competitions, have 18 points, two ahead of champions Borussia Dortmund who are fifth after a goalless draw against VfB Stuttgart on Saturday.
Bayern Munich beat Hamburg SV 3-0 on Saturday to go seven points clear at the top with 27.
"I am very satisfied with the mentality of my team," said Sascha Lewandowski who coaches the team along with Sami Hyypia.
"We react very well to setbacks but our play and tactics seem to come and go. That has been the case recently and it was the case again today."
Sidney Sam was set up by Stefan Kiessling as he chipped the ball in after 16 minutes against Fortuna who have now lost four league games on the trot.
The visitors equalised through Nando Rafael's deflected header off in the 40th minute but had only 40 seconds to celebrate as Andre Schuerrle, who had earlier rattled the crossbar, thundered the ball in from six metres for Leverkusen.
The home team suffered another setback when substitute Simon Rolfes got his marching orders two minutes after coming on following a hard tackle from behind on Adam Bodzek in the 65th.
Leverkusen then made it 3-1 when Gonzalo Castro tapped the ball in from close range a minute later after Daniel Carvajal had pounced on a Fortuna mistake.
Bodzek drilled the ball in from 24 metres with four minutes to go to set up a nervous finale but Fortuna eventually ran out of time.
In Sunday's only other game, Werder Bremen captain Aaron Hunt scored twice to earn a nervous 2-1 victory over Mainz 05.
Hunt fired them into an 10th-minute lead with an unstoppable 12-metre drive before Hungary international Adam Szalai joined Bayern's Mario Mandzukic on top of the Bundesliga scorers' list by heading in his eighth goal of the season for Mainz in the 64th minute.
Skipper Hunt then curled a left-footed free-kick over the wall and past keeper Christian Wetklo who crashed face-first into the post in the 85th minute.
Schalke 04 slumped to a 3-2 defeat at Hoffenheim on Saturday to stay second on 20 points along with third-placed Eintracht Frankfurt who drew 1-1 with Greuther Fuerth on Friday.
