The 15-time European champions appeared on the verge of a disappointing defeat in Greece after falling behind twice. However, Kylian Mbappe restored parity before Valverde delivered the decisive blow in the closing moments.
Madrid entered the encounter seeking a fourth consecutive victory in the competition's league phase but were immediately challenged by an energetic AEK side.
The hosts took an early lead through Aboubakary Koita, who produced a powerful finish to put the Greek outfit ahead and send their supporters into celebration.
Madrid responded through Jude Bellingham, who showcased remarkable technique to level the contest in the 32nd minute. The England international cleverly redirected the ball into the net with a stunning backheel, leaving the goalkeeper with little chance.
The goal also saw Bellingham achieve a remarkable milestone. At 23 years and 128 days, he became the youngest player to score in seven consecutive Champions League seasons, surpassing teammate Mbappe's previous record.
Despite the equaliser, AEK continued to threaten and refused to surrender their attacking ambitions. Their persistence paid off with 15 minutes remaining when Stavros Pilios restored their advantage.
Pilios had earlier produced a crucial defensive intervention to deny Mbappe a scoring opportunity. He then joined the attack and finished confidently at the near post, putting AEK within touching distance of a memorable victory.
Madrid responded swiftly, however, with Mbappe finding the back of the net three minutes later. The French forward arrived at the far post to convert a delivery from Denzel Dumfries, bringing the visitors level once again.
With the match seemingly heading towards a draw, Valverde produced a moment of brilliance in stoppage time. The Uruguayan midfielder unleashed a thunderous long-range effort that flew past the goalkeeper, completing Madrid's comeback and securing all three points.
The result maintained Madrid's unbeaten start to the Champions League campaign, strengthening their position among the leading teams in the league phase.
AEK's frustration boiled over after the final whistle, with Koita receiving a red card as tensions escalated following the narrow defeat.
