Hearts' lead is cut to one point with two games remaining, and they have to travel to Celtic Park on the final day of the campaign on Saturday.
Maeda's return to form has spearheaded Celtic's late charge for a 14th title in 15 years. Six of the Japan international's 14 goals this season have come in the last four games.
"Extraordinary performance from Daizen Maeda. His second goal was just unbelievable," said Celtic interim boss Martin O'Neill.
"We're still in it, we're still fighting, and that's the most important thing to come out of today.
Three consecutive defeats have knocked Rangers out of contention for the title and ensure Danny Rohl's men will finish third.
"We had a great position before the split, and this is hard to take and we have to improve and develop quick," said Rohl.
"I will take a lot from the last three games to be prepared the best way possible. I will lead this group, and I am clear about what we have to improve."
The visitors got off to a perfect start when Tottenham loanee Mikey Moore took advantage of slack Celtic defending to tap in on nine minutes.
Martin O'Neill's men responded quickly to level when Yang Hyun-jun fired home Arne Engels' low cross.
Maeda then scored twice in three minutes just before the hour mark to secure Celtic's first league win over Rangers since September 2024.
The forward turned in Kieran Tierney's cross before a sensational looping overhead kick dropped into the far corner to spark manic scenes of celebration among the 60,000 crowd.
Hearts have led for almost the entire season as they aim to become the first side outside the Old Firm to win the Scottish title for 41 years.
The Jambos could still seal the title on Wednesday with victory over Falkirk if Celtic lose at Motherwell.
Any other combination of results will mean the title is on the line when Hearts travel to the East End of Glasgow in six days' time.