In for Rafinha, Ousmane Dembele aimed to make the most of his chance when he ventured forward from the right before cutting back to take a left-footed shot to force Samir Handanovic to a save.
Inter’s first chance came on 18 minutes when Asamoah bombed down to left to combine with Ivan Perisic who played a return pass to the box before seeing the Ghanaian miss from close range.
Luis Suarez brought down a high ball inside the box and used his inside-step to try to find the far corner, but the effort went wide.
The Catalans started to dictate play and with it came the chances as Milan Skriniar was forced to clear a Phillipe Coutinho shot off his line.
It was followed by another low drive from the visitors with the same man forcing Handanovic to get down for a save.
Closer to the break, a ball unexpectedly felt to Suarez after a shot from inside fell to his grasp but Handanovic again pulled off the save.
In the second half, the Nerazzurri started with more promise and a flick header from Stefan De Vrij off a free-kick found the top of the side-netting.
After getting goal-side, Coutinho shot from close range brought the best out of Handanovic once again, while Vecino’s instant half-volley went over the top.
On the counter, Barca missed another chance when Ivan Rakitic failed to beat Handanovic from point-blank range.
The battle between Coutinho and Handanovic continued when the Brazilian took two defenders out of his way to draw another save from the Slovenian.
Inter created an exciting move when Perisic flicked over a diving Sergi Roberto to run down the wing and pick out an on-rushing Matteo Politano who headed narrowly wide.
Dembele found space on the far side to toss and turn out of challenge before taking a crack at goal which Handanovic blocked away with Suarez firing the rebound to the side-netting.
The first change of the game, saw Borja Valero replacing Radja Nainggolan, while Arturo Vidal made way for Arthur Melo for Barca later on.
As both sides kept possession and soaking up the pressure, Barca took the lead later on when Malcom came off the bench to finish off a counterattack for his first goal since arriving.
However, the Nerazzurri struck back and it was Mauro Icardi turning Clement Lenglet to beat Marc Andre Ter Stegen.
The Spaniards searched for a way back but in the end to try and clinch Group B, but settled for a draw instead.