Sougou scored on either side of the break (6th and 78th minute) to help Mumbai grab three points.
While Bobo scored the lone goal (81st minute) for Hyderabad, who suffered one more loss.
Mumbai started on an attacking note and in the opening minute itself Kevyn Serge Angoue sent a cross to Diego Carlos, who made a run down the left flank and beat his man and took a shot, which was safely punched away by rival custodian Kamaljit Singh.
Hyderabad also had a chance in the second minute when Rohit Kumar passed the ball to skipper Marcelo Pereira, who found Bobo in the box.
Bobo took a left-footed shot, but that went wide.
However courtesy Modou Sougou, the hosts took 1-0 lead in the sixth minute.
Subhasish Bose made an interception on the left flank and passed it to Carlos, who made a run inside the box and squared to Sougou, who slotted home with a right-footed shot.
Hyderabad had a chance in the 22nd minute, but Bobo's header sailed above the bar.
The hosts kept the Hyderabad goal-keeper busy as they kept creating chances after chances, the most poignant one in the 42nd minute.
At the half-way mark, Mumbai was 1-0 ahead.
After the change of ends, a chance for Hyderabad came in 52nd minute, when Giles Barnes lobbed into the box on a free kick from the left.
Shankar Sampingraj headed to Adil Khan and the ball fell to Bobo, who hit it on target on an empty net.
The ball, however, hit defender Matthew Kilgallon's back and was then safely cleared by Mumbai players.
Hyderabad had another close chance in the 66th minute, when Bobo passed the ball to skipper Pereira, whose left- footed shot hit the pole.
And Sougou doubled Mumbai's lead in the 78th minute.
Pratik Chaudhari passed the ball to Bidyananda Singh, who lobbed it towards the right-hand side of the 18-yard box for Sougou.
A A composed Sougou then saw the goal-keeper coming off the line and chipped it over his head to take the hosts 2 -0 ahead.
However, just three minutes after that Bobo pulled one back for Hyderabad.
Ashish Rai played it in behind the Mumbai back-line and Bobo slotted home with a neat finish.
However, that goal wasn't enough for Hyderabad to avoid defeat.