Mellor had a great start to his loan period when he set up Roberts to open the scoring after only two minutes. Former Red David Thompson, who was also making his Wigan debut, then added a second to make it 2-0.
Middlesbrough pulled two goals back in the second half before Mellor struck in injury time to send his new supporters home happy.
Wigan manager and former Red Paul Jewell said: "I told the two lads before the game that new players of mine do tend to score on their debuts. Mellor waited until the 90th minute before doing it today.
"I'm delighted for both lads and for the team because we played some good football and deserved the points."