Antonio Conte’s side had the better chances in the first half, but the woodwork came to Barca’s rescue on two occasions as Willian hit both uprights.
The Brazilian eventually opened the scoring with a sweet strike in the second half, but a mistake at the back led to an equaliser from Lionel Messi to put Ernesto Valverde’s men in the driving seat for the second leg in Spain.
The Blaugrana bossed possession in the first half. but they created very little and failed to get a shot on target.
The first couple of chances came the way of the hosts, with Eden Hazard flashing a left-footed shot just wide of the left post from 20 yards out on five minutes after cutting inside from the right, before Antonio Rudiger steered a header well wide of the same upright from a ninth-minute corner.
Paulinho should have done better at the other end seven minutes later with a header that went wide of the left post from Messi’s clipped cross on the left.
Barca had the upper hand in the opening half-hour, but the Blues finished the half on the front foot. Marcos Alonso drew a routine save out of Marc-Andre ter Stegen with a free-kick from 25 yards out on 31 minutes, before Willian smacked an effort against the right post from 21 yards out two minutes later.
Gerard Pique could only direct a header wide of the right post from a corner under pressure from Rudiger in the 38th minute, while Willian struck the left post three minutes later with a fierce shot from 20 yards out after Hazard won the ball back.
Hazard then went close two minutes before half-time from Cesc Fabregas’ free-kick that was only half-cleared, with the Belgian firing over on the volley after running onto the ball at pace.
Andres Iniesta was given space on the left to shoot four minutes into the second half, but he fired well wide of the left post on his left foot from 22 yards out.
However, Willian was not to be denied as he received a short corner from the left and shifted the ball to his right before lashing a shot inside the right post past a stationary Ter Stegen from just outside the area on 62 minutes.
The Catalan giants were let back in 13 minutes later when Iniesta collected a poor pass across the box from Andreas Christensen and he cut the ball back to Messi, who slotted past Thibaut Courtois from 16 yards out with a low finish inside the left post.
Both teams pushed for a winner in the closing stages, but neither keeper was tested which meant that Barca took a valuable away goal into the second leg at the Camp Nou.