Luton leapfrogged Everton into 17th place with a fantastic 4-0 victory at home to Roberto De Zerbi's high-flying side, who fell behind to Adebayo's first inside the opening minute.
Kenilworth Road was rocking shortly afterwards as Chiedozie Ogbene doubled the lead before Adebayo struck either side of the interval to complete a famous win for Rob Edwards' men.
"His work-rate has always been great but he's seeing how important it is to press hard, press the goalkeeper, press his man. He does that tirelessly," Edwards said of Adebayo.
"He's got a really high ceiling. If he stays focused and keeps working hard, he can go a long way and have a really good career."
Edwards was delighted with his side's performance in the battle against relegation, but added: "It's still only three points.
"We've got to keep our foot down. We've got to be at full-tilt every day, otherwise we've got no chance."
Everton slipped into the drop zone after drawing 0-0 in a forgettable contest at Fulham.
Substitute Taiwo Awoniyi halved the deficit late on but the Gunners saw it out to take the three points.
The win was a far cry from last season, when May's unexpected 1-0 defeat at the City Ground brought an end to Arsenal's title challenge.
"I am really happy with the performance and the result," said Gunners boss Mikel Arteta.
"We saw what happened last year and we wanted to put it right, we wanted to generate some momentum in the league and we did that.
"The performance was very good, we completely dominated the game.
"We had to be patient but we always had an eye to the opponent, we didn't allow them to run."
Aston Villa's 17-match unbeaten run at home in the league came to a shuddering halt as they were thrashed 3-1 by Newcastle.
A double from defender Fabian Schar had the away side in charge at the break and they extended their lead through an Alex Moreno own goal - with Ollie Watkins hitting a late consolation for fourth-placed Villa.
Ben Brereton-Diaz put the Blades ahead in the first minute and they retook the lead through James McAtee after Eze had levelled for the hosts.
England international Eze was again on hand to equalise, with Michael Olise - who had provided the assists for both Palace goals - hitting the winner to take some of the heat off under-pressure boss Roy Hodgson.