After a game that had plenty of industry but precious little quality, Newcastle substitute Jacob Murphy came close to giving the home side the lead as he smacked a right-foot shot off the crossbar in the 83rd minute.
It was to prove a costly miss as Villa striker Ollie Watkins latched onto a Matt Targett cross three minutes later and his header deflected off Clarke into the net.
Lascelles then popped up to head home in the fourth minute of stoppage time to grab a point that leaves Newcastle in 16th spot on 28 points from 28 games, two points above the relegation zone. Villa are ninth on 41 points from 27 matches.
“Over the course of the game, I wouldn’t say it was a fair result — I thought we were the better team, I thought we had the better chances,” Lascelles told BT Sport.
“We’ve got a really tight group [of players] and we all want to succeed. I think the performances have been a lot better compared to the start of the season.”