Jimmy Shan’s Young Lions will now look to make the most of home advantage in next month’s second leg of the round two tie, after a closely-fought contest in the city of Korce deep in the Morava Mountains.
Ben Broggio saw a penalty saved before Scotland under-21 international Wilson fired Villa ahead eight minutes before half-time.
But the visitors were not in front for long, with Ensar Beqiri quickly levelling for the Albanian champions Skenderbeu. Neither team was able to find a winner in the second half.
Villa are playing in the Youth League for the second straight season having reached the last-16 of last year’s tournament, before being knocked out by the eventual winners Barcelona.
Their starting line-up in Albania featured the bulk of the team which won three domestic trophies last term, including the FA Youth Cup.
After a scrappy opening, Villa were handed the perfect chance to take the lead when French referee Antoine Chiaramonti pointed to the spot after Leon Routh was pulled down in the box at a corner.
But though Broggio struck his spot-kick well, Skenderbeu skipper Amarildo Dervishi was equal to it, springing to his left to make the save.
Villa’s disappointment proved short-lived as Wilson soon fired them ahead. Aidan Borland dinked a pass into the box and the striker rounded Dervishi before slotting into an empty net.
Having worked hard to take the lead, the visitors then almost immediately let it slip. A long throw-in caused uncertainty in the box and Beqiri finished past Villa keeper Sam Proctor.
Beqiri went close again either side of the break as the home side grew in confidence.
Villa’s next big chance fell to scorer Wilson but he was unable to get any power on his header from Cole Brannigan’s cross.
The forward then sent another effort over the bar after latching on to Jamaldeen Jimoh-Aloba’s pass.
It was Villa who finished the stronger but on a tricky pitch the final pass frequently eluded them, Wilson seeing appeals for a penalty waved away after tumbling in the box.
The teams meet again for the second leg at Bodymoor Heath on Wednesday, November 5 (kick-off 1pm), with either AZ Alkmaar of Lincoln Red Imps of Gibraltar awaiting the winners in the third round.