Liverpool, however, fell to a surprise 3-2 defeat at Fenerbahce on a dramatic night of action, while Manchester City battled to victory over RB Leipzig by the same score after twice blowing leads, and Como beat Lens 9-1.
Last season's runner-up Arsenal beat Slavia Prague 2-1.
Madrid joined back-to-back defending champions Paris Saint-Germain as the only other team to have a 100 per cent winning record after four games played in this season's competition. But that perfect start was put under serious threat in Greece.
The record 15-time European champions twice went behind at Allwyn Arena and needed Valverde's long-range strike in the 92nd minute to seal victory.
"Of course, I prefer to win more comfortably, but these games in the final minutes — only we can win them," Madrid coach Mourinho told broadcaster Movistar.
Madrid also needed a late rally to beat Roma 4-3 last month, scoring three goals in the last 10 minutes, including a 90th minute winner from Antonio Rudiger.
AEK led through Aboubakary Koita in the first half before Jude Bellingham leveled with a back heel.
Stavros Pilios put the home team 2-1 ahead in the 75th, but Kylian Mbappé equalised three minutes later.
Mbappé then hit the bar before Valverde's dramatic winner.
"The players have courage. I'm very lucky to have players of this quality. Very lucky," Mourinho said.
Liverpool twice blew the lead against Fenerbahce before losing for the first time in this season's Champions League.
Trey Nyoni and Alexander Isak gave the Merseyside club the lead in each half, with former Manchester United striker Mason Greenwood and Archie Brown leveling for Fenerbahce on each occasion.
Vedat Muriqi struck the winner in the 89th as Liverpool fell to back-to-back losses in all competitions following defeat to Arsenal in the Premier League on Sunday.
"The main reason I can find for why we lost this game is we conceded from three set pieces," Liverpool coach Andoni Iraola said.
"We knew it was one of the strengths of Fenerbahce. We concede from a free-kick, a corner and even from the long throw at the end. It's frustration because it's a difficult place to come here and play."
Victory will have been particularly sweet for Fenerbahce interim coach, former Liverpool striker Dirk Kuyt.
Erling Haaland came back to haunt Leipzig and drag City over the line after being pushed to the limit at Red Bull Arena.
The Norway striker has scored 13 goals against Leipzig and came up with the winner in the 78th after City twice failed to hold onto the lead.
First-half goals from Noni Madueke and Viktor Gyokeres put Arsenal on course for victory at Slavia Prague and despite conceding in the 90th, the Premier League champions sealed a 2-1 win.
Tasos Douvikas scored a hat-trick and Cesc Fabregas' Como routed Lens 9-1 to make it three victories in four matches of their debut season in the competition.
Douvikas has scored in all four of Como's matches.
Napoli coach Massimiliano Allegri was in crisis following a 4-1 loss at Porto.
It was Napoli's third loss in four matches of the league phase; and the Partenopei are struggling in Serie A, too — having been beat 2-0 at Juventus on Sunday.
Porto have a perfect 10 wins in 10 matches to lead the Portuguese league but had lost their opening three matches in the Champions League.
Konstantinos Karetsas' first goal for Borussia Dortmund gave the 1997 champion a 2-1 win over Real Betis.
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