Danny Ings tucked away in his first European goal on the stroke of half time to put the Hammers in front, but the hosts restored parity just before the hour mark courtesy of a sweet strike from Hugo Cuypers.
David Moyes's side were second best for large spells of the second half, with Gent posing the greater threat in the final third, but the Hammers eventually held on for a share of the spoils and remain in the tie heading into the second leg at the London Stadium next week.
West Ham made a confident start and controlled proceedings in the opening exchanges, but Gent gradually grew into the game and had the first two attempts on goal inside the first 15 minutes.
After a tame long-range effort from Julien De Sart was comfortably saved by Alphonse Areola, Jordan Torunarigha saw a towering headed glide over the crossbar following a corner.
Flynn Downes and Angelo Ogbonna were both booked midway through the first half for late challenges, and the latter will now miss the second leg at the London Stadium through suspension.
Gent enjoyed a sustained period of possession in West Ham's half, with their main threat coming from set-pieces, but the Hammers also caused problems from dead-ball situations and thought they had made the breakthrough five minutes before the break.
An out-swinging corner from Jarrod Bowen was fumbled by Gent goalkeeper Davy Roef inside the six-yard box before Nayef Aguerd bundles the ball into the net, but the goal was eventually disallowed by VAR as the ball touched the arm of the Hammers defender before crossing the line.
West Ham had the ball in the net again in the fifth minute of first-half stoppage time when Vladimir Coufal caught Gent's defence napping with a quickly-taken throw-in towards Bowen, who picked out Ings with a first-time cross to slot home from just a few yards out.
VAR intervened again, this time to check for a possible offside in the build-up, but the goal was allowed to stand and the Hammers entered the half-time interval a goal up.
Both teams made a relatively quiet start to the second half, but the Ghelamco Arena erupted when Cuypers netted a 56th-minute equaliser for Gent out of the blue, firing a left-footed shot beyond Areola after Alessio Castro-Montes started the move with a neat one-two with Gift Orban on the edge of West Ham's penalty area.
Cuypers has now scored six goals in his last five games in all competitions and Gent's top scorer has increased his goal tally for the season to 24, including five strikes in the Europa Conference league.
Hein Vanhaezebrouck's side came close to taking the lead on the 68-minute mark when Castro-Montes dragged a shot wide of the far post from inside the area, before Bowen poked a weak effort off target at the other end after receiving a brilliant through-ball from substitute Lucas Paqueta.
The momentum was with the hosts heading into the final 10 minutes, and Areola had his heart in his mouth when a speculative acrobatic effort from Orban looped onto the top of Hammers crossbar.
Castro-Montes and Tarik Tissoudali also came close with efforts inside the area, before a dramatic finale saw Kamil Pistkowski sent off deep into stoppage time for what was initially deemed a late tackle on Pacueta to deny a goalscoring opportunity.
However, following a VAR review and a look at the pitchside monitor, the on-field referee reversed his decision with no red card of free kick awarded to the delight of the home supporters.
Gent deserve plenty of plaudits for taking the game to West Ham, who were somewhat fortunate to come away with a draw after failing to match the hosts' energy and intensity levels throughout the contest.
West Ham will not shift their focus back to the Premier League with a tricky home encounter against leaders Arsenal on Sunday, while Gent return to Belgian top-flight action with a trip to Mechelen.