Jed Wallace gave the hosts an eighth-minute lead before Tyler Blackett was shown a straight red card for a strong tackle on the goalscorer a minute later.
Reading pushed in the second half and John Swift hit the crossbar with a 72nd-minute free-kick.
But any chance of a Reading equaliser was extinguished when Leandro Bacuna received a straight red card with two minutes left after he appeared to kick out at Shane Ferguson.
It was tough on the Royals, who despite those dismissals gave Gomes plenty to be encouraged by as they composed themselves following an early Millwall barrage.
Neil Harris' Lions made it more difficult for themselves than it could have been, but eventually got their first win since October 27.
Gomes took over from Scott Marshall – who had been in caretaker charge since Paul Clement's sacking earlier in December – after last Saturday's 1-0 home loss to Middlesbrough with the immediate task of trying to end a disappointing run.
The game began disastrously for the visitors when Wallace fired home a direct free-kick following Omar Richards' foul on Tom Elliott, and then Blackett paid for his rashness to leave his side in real trouble.
Ryan Tunnicliffe saw his shot from 10 yards deflect over as Millwall kept up the early pressure.
To Reading's credit they did settle into the game, though they had only Swift's 22nd-minute shot that was saved by Jordan Archer low to his right to show for their efforts in the first half.
Six minutes after the break, Danny Loader shot straight at Archer, before Millwall's Ryan Leonard was just off target with an effort from 25 yards.
Bacuna burst into the box in the 57th minute before shooting wide as Reading continued to push players forward. It was Millwall fans who were getting frustrated.
And their nerves were frayed again as Yakou Meite raced clear before Jake Cooper made a block in the box.
The visitors went close to an equaliser with 18 minutes left when Swift's fierce free-kick from 35 yards came back off the crossbar, but Reading's hopes ended with Bacuna's departure.