Tau, who turns 29 on Saturday, scored after eight and 55 minutes of the first leg of the semi-final in an empty national stadium on the outskirts of Tunis, two weeks after mob disturbance there.
With a third goal in 75 minutes, Mahmoud Kahraba clinched a surprisingly easy victory for the record 10-time African champions.
The return match will be held in Cairo on May 19, and Ahly will almost certainly go to a two-leg title decider either Wydad Casablanca of Morocco or Mamelodi Sundowns of South Africa.
Defending champions Wydad, who defeated Ahly in the 2022 final of the main CAF club championship, will host Sundowns in the other opening leg on Saturday.
Tau, who plays on the right side of midfield for Ahly, has been consistently impressive this season, and his brace in Tunisia brought his Champions League goal count this season to four.
He opened the scoring when unmarked just inside the penalty area, with a shot that deflected off the knee of custodian Mohamed Debchi, who was filling in for the injured Moez Ben Cherifia.
If his first goal was a stroke of luck, Tau extended his lead with a superb solo effort that effectively placed the outcome beyond dispute.
Mohamed Tougai tracked him across the ground just beyond the box before unleashing a shot into the corner of the net with Debchi stranded.
Tau left Sundowns for Premier League team Brighton in 2018, who leased the winger to three Belgian clubs before selling him to Ahly two years ago.
Hussein el Shahat set up the last goal with a low cross to the far post, where the unprotected Kahraba tapped in his fifth Champions League goal of the season.
Ahly has won twice and drawn once in four visits to the Tunisian national stadium in the Champions League semi-finals.
As expected, Mohamed Ali Ben Hammouda was Esperance’s main danger, and shortly after Tau gave Ahly the lead, the Tunisian was barely off target with a low-deflected attempt.
Yassine Meriah headed over from the resulting corner when he could have forced a save from veteran custodian Mohamed El Shenawy.
That was the closest Esperance came to scoring, and by the final whistle, they were a demoralised team that knew their hopes of winning the Champions League this season were fading.