Both goals came from Ivorians with midfielder Fousseny Coulibaly giving the Tunisian outfit a 44th-minute lead in Rabat and centre-back Cheikh Comara equalising 11 minutes from time.
Wydad and Esperance meet again next Friday in the Tunis suburb of Rades to decide who wins the elite African club competition and becomes $2.5 million (about 2.2 mn euro) richer.
Spectators and TV viewers will hope for some free-flowing football in the return match with the first leg never reaching great heights due to constant fouling by both sides.
Drawing away makes Esperance favourites to emulate TP Mazembe of the Democratic Republic of Congo, Enyimba of Nigeria and Al Ahly of Egypt and win back-to-back titles.
The first leg stalemate was not surprising as three of the previous four meetings between the clubs in the Champions League were also drawn.
A cagey first half before a 50,000 crowd at the Stade Prince Moulay Abdellah in the Moroccan capital suddenly came to life as half-time approached.
Coulibaly scored his second goal of the competition with a close-range shot after his header had been parried off the goalline by Wydad goalkeeper Ahmed Tagnaouti.
Ayoub el Amloud thought he had levelled in first-half stoppage time only for his effort to be ruled out for handball by Ismail el Haddad after the Egyptian referee watched VAR replays.
Wydad were reduced to 10 men just four minutes into the second half when captain and midfielder Brahim Nakach received a second yellow card and was sent off.
There was more VAR disappointment for the hosts soon after when penalty appeals were rejected with the referee deciding the ball hit the shoulder of an Esperance defender, not his hand.
But Wydad never stopped trying and were finally rewarded when Comara completed a brilliantly executed move by powering a header past helpless goalkeeper Moez Ben Cherifia.
El Haddad took a free-kick that was nodded on by Salaheddine Saidi in a crowded goalmouth and Comara scored his first Champions League goal this season with an unstoppable header.
Mohamed Ounajem could have won the match for Wydad in stoppage time but his hastily struck close-range shot flew over.
Wydad are coached by 69-year-old Tunisian Faouzi Benzarti, who won the competition with Esperance in 1994, the first of his five successes in African club finals.