It was a backs-to-the-wall performance from the Premier League highflyers for the majority of the contest, however the visitors managed to grow into the match during the second period.
Striker Brian Brobbey had the best of the chances for the four-time European champions, although Emiliano Martinez was able to keep a vital clean sheet.
The match descended into a scrappy affair in the closing stages as both sides saw players sent off, with Ezri Konsa and Tristan Gooijer receiving their marching orders.
After recording a much-needed 2-0 victory over FC Utrecht on Sunday afternoon as Ajax seek to rescue a top-four Eredivisie finish from a largely-disappointing campaign, John van't Schip named an unchanged side, with England international Jordan Henderson playing his sixth match for the Amsterdam giants.
Unai Emery - unlike his Dutch counterpart - decided to shuffle his pack following three-straight Premier League successes, making five changes to the side which dramatically won at Luton Town on the weekend, with academy graduate Tim Iroegbunam earning his maiden start of the season alongside Arsenal-linked Douglas Luiz in the engine room.
With a second-leg clash scheduled next Thursday in the West Midlands, Villa set out to be solid on their travels in this match, with the likes of Youri Tielemans tracking back religiously in the first half, to the point where it was not unusual to see the visitors in a flat six across the backline.
Villa's most-notable attack of the opening 45 minutes arrived early on when Moussa Diaby hit a strike from the left to sting the palms of Ajax goalkeeper Diant Ramaj, but in truth the former Bayer Leverkusen man may have been better off finding a teammate in an advanced position.
As a couple of sides in the Premier League have done to good effect over the course of this season, the Dutch hosts were constantly looking to play lone-striker Brobbey behind a high Villa backline, however World Cup winner Martinez was quick out of his goal to collect on numerous occasions.
The best chance of the first period from either side arrived at the galloping feet of 22-year-old Brobbey, who was sent through on goal but only managed to strike his effort into the side netting after Konsa had raced back to apply some pressure on the Ajax academy graduate.
Following the arrival of the more attack-minded Matty Cash in place of Pau Torres at half time, Villa were a greater attacking threat in the opening moments of the second half without seriously testing the Ajax net.
Boasting his wealth of European experience, Emery will have realised that keeping the tie level ahead of next week's second leg in Birmingham would be a respectable feat, however the visitors made changes which suggested that they were pushing for a victory, with John McGinn and Leon Bailey joining the action for the final 30 minutes.
A raft of misplaced and heavy passes plagued a second half which neither side managed to take control of fully, however Ajax did string a move together through Borna Sosa and Kenneth Taylor, with the latter's first-time effort in the box forcing a smart stop at the near post from Martinez.
With the game in danger of fizzling out in the closing stages, a second yellow card for Villa centre-back Konsa changed the complexion of the final 10 minutes, with the 26-year-old judged to have pulled back former Middlesbrough marksman Chuba Akpom as he raced through on goal.
Emery's troops did not burden a numerical disadvantage for long, though, as Ajax were soon down to 10 men three minutes later, with Gooijer collecting his second caution of the match for a poorly-timed tackle on Villa substitute Nicolo Zaniolo.
Despite a late flurry of pressure from the Villans in added-on time, they had to settle for a hard-fought draw in the Dutch capital, setting themselves up nicely for the second leg at Villa Park next week.
Ajax were able to hold on for their first clean sheet in European competition this season and will host Fortuna Sittard in the Eredivisie before trekking over to England next Thursday with the tie perfectly poised.