Luka Jovic enhanced his growing reputation by scoring his 26th goal of the season, a fabulous header that put Eintracht ahead after 23 minutes of the first leg.
But Maurizio Sarri's men turned the tide and Pedro struck amid a flurry of late first-half pressure.
David Luiz hit the crossbar with a free-kick and the rested Eden Hazard was sent on after the hour mark to try to force an elusive winner, although the Premier League side remain well positioned to seal their place in the final in Baku.
Roared on by a ferocious home crowd, Eintracht made a positive start and captain David Abraham should have raised the roof when he blazed over unmarked from Danny da Costa's 21st-minute set-piece.
Star forward Jovic proved typically more reliable from a far trickier chance, brilliantly glancing Filip Kostic's left-wing cross into the bottom-right corner.
Eintracht's poise deserted them during the closing minutes of the first half and, after twice going close himself, Ruben Loftus-Cheek showed supreme strength and close control as he set up Pedro to lash home.
The England midfielder was to the fore again in the 54th minute, powering smoothly through the Frankfurt half and exchanging passes with Pedro, although he could not find the finish to match.
Chelsea were in command as the hour approached and David Luiz cracked a free-kick from 25 yards against the bar, before Hazard entered the fray in place of Willian in the 61st minute.
Eintracht goalkeeper Kevin Trapp parried to deny Loftus-Cheek the goal his endeavours deserved and held a David Luiz header.
Abraham nodded an 85th-minute chance over - it was Eintracht's first opening for some time and would have been an incredibly fortunate winner.
What does it mean? Advantage Chelsea
Despite conceding the opening goal for the first time in their Europa League campaign, Chelsea turned in a performance of impressive authority as all Sarri's key components clicked into gear. After failing to drive home a high-tempo start fuelled by their incredible supporters, the sense is that Eintracht have missed their chance.
Loftus-Cheek should not return to back-up role
Four of Loftus-Cheek's five Premier League starts this season have come since the beginning of April. It was easy to understand why the 23-year-old is enjoying a newly elevated status under Sarri as he provided in a dominant, match-turning display.
Fernandes overrun as Frankfurt fade
Gelson Fernandes' early eagerness to fly into duels exemplified the hosts' impressive start. However, the Switzerland international increasingly became a helpless bystander as Loftus-Cheek got control of midfield and Jorginho dictated proceedings despite a nasty clash of heads with Sebastian Rode. In contrast to the bandaged Italy star, Fernandes completed only 57.1 per cent of his passes and collected a booking before being substituted in the 73rd minute.
Key Opta Facts
7 - Pedro's seven goal involvements in the Europa League this season (4 goals, 3 assists) have all come in his last six starts in the competition. Up. #SGECHE— OptaJoe (@OptaJoe) May 2, 2019
- Chelsea are unbeaten in their last 16 Europa League games, a record in the competition since it was rebranded in 2009-10.
- Eintracht have played 11 Europa League games at Commerzbank-Arena, winning eight and drawing three. They have not been behind for a single minute in those matches.
- Just one of the six teams to draw the first leg of a Europa League semi-final away from home has been eliminated, Celta Vigo in 2016-17 (knocked out by Manchester United).
- Chelsea have scored the most goals (31) and had the most shots (217) in the Europa League this season.
Fourth in their respective leagues, Chelsea and Eintracht can ill afford slip-ups against Watford and Bayer Leverkusen this weekend. This time next week, the domestic route to the Champions League will be the only avenue one of them still has open.