Baniyas found their form in the second half but it was too little, too late against Diego Maradona's Al Wasl side.
Maradona full of praise for his 'family'
Two goals in the first 10 minutes for the Dubai side, who have now taken a maximum six points from their first two league games, set up this victory, sending them two points clear at the summit.
David Trezeguet made his league debut for Baniyas, but it was a frustrating night for the Frenchman who missed a couple of excellent chances to score; although he needed only four minutes to make an impression on proceedings.
A cross from Amer Al Hammadi travelled 45 yards and found the former Juventus man lurking on the left-hand side of the box.
The World Cup and European Championship winner hit a first-time volley with his left foot that cannoned off Rashed Essa, the Wasl defender, and forced goalkeeper Majed Naser into a smart save to prevent what would have been an own goal.
Despite that early chance, it was the visitors who took the lead two minutes later.
In what looked a rehearsed move, Mariano Donda's corner was aimed towards the edge of the box where Darwish Ahmed arrived at speed to send a powerful header into the top corner.
Nine minutes later, Wasl doubled their lead.
Saoud Saeed showed great pace to get down the left wing and his low cross into the middle was turned home expertly by last week's hat-trick hero, Juan Manuel Olivera, from 10 yards out.
Maradona, who punched the air in delight at the final whistle, was full of praise for both sides after the game.
"The two teams, Al Wasl and Baniyas, shared the game," he said. "Both sides showed up well in the match.
"Baniyas tried to take advantage of the high ball, but my defenders did really well to stop these passes.
"The team played well and they deserved to win this match. I was so pleased for them. All the players are my family because I am away from own family."
Baniyas, who struggled badly in the first half, were back in the game five minutes after the break when Al Hammadi got on the end of Andre Senghor's knock-down to direct a half-volley into the back of the net.
Trezeguet passed up a great chance to equalise almost immediately after when he sent a shot wide from inside the box.
Jorvan Vieira was asked after the game whether he felt his job was under threat because of Baniyas' slow start to the season.
"That is not up to me," said the Brazilian.
"They [the board] can decide whenever they want. Only in England do you have coaches for 20 years."