Substitute Kalajdzic steered in a header from Pedro Neto’s cross to earn Wolves their first points of the season, having ridden their luck as Everton spurned numerous opportunities to score first.
Everton looked like the more dangerous team but were left waiting for their first goal and point of the campaign in another demoralising defeat that was a carbon copy of their opening-day loss to Fulham. The Merseysiders are rooted to the bottom of the standings having lost all three of their matches this season.
Wolves are 15th with three points.
Both teams had goals disallowed earlier but Wolves finally found the breakthrough with their only shot on target in the match.
“I think it’s massive, it’s important for us that we gain confidence. I think we’ll get even better,” Kalajdzic said. “I was out for almost a year and now it’s about step-by-step. I dreamed of being healthy. Goals come and go.”
Everton manager Sean Dyche must wonder where to go from here, with his side’s troubles in front of goal plain for all to see.
This is already looking like a season of toil after back-to-back relegation battles saw them narrowly avoid the drop, and the boos that rang out around the ground at the final whistle suggest the supporters have lost what little patience they had left.
Everton defender James Tarkowski flashed a shot into the side-netting from a tight angle when he should have hit the target, and Arnaut Danjuma volleyed wide from Nathan Patterson’s cross.
A mix-up between Tarkowski and goalkeeper Jordan Pickford gave Fabio Silva a one-on-one chance but he put his shot wide of the post in a big miss.
Pickford then made an astonishing stop from point-blank range when the ball appeared to ricochet off a teammate in the six-yard box and seemed destined for the net.
Minutes later Wolves goalkeeper Jose Sa pulled off an extraordinary save from close range to deny Abdoulaye Doucoure’s header, a vital intervention that allowed for Kalajdzic’s late winner.
“It is very difficult to take,” Doucoure said. “I think we were the better team, but we need to be clinical. We need to be more aggressive around the box.”
“The supporters come each week to support us and we need to give something back. We need to take responsibility. The team is fighting, but we need more from each other.”