The 19-year-old's first-half strike, his first of the season, proved enough for the O's to progress in the competition, leaving Slade in a high spirits.
The O's boss said: "He started the match and has had another good game for us. They are all really important minutes for him on the pitch and he caps his performance with a great goal.
"With the ball in front of him, I think he's quite a threat and how we set up, which was slightly lopsided, gave him time and space to get down the side and he seemed to be enjoying himself."
The winner came after 25 minutes when Odubajo stole into the box to meet a Dean Cox cross and stab the ball home from close range. David Mooney had one ruled out for offside as the home side controlled proceedings.
"It was a good move and we played some good football at times," said Slade of the winning goal. "Yes, there were a few stray passes, we were a bit patchy at times and our decision-making wasn't absolutely fantastic but I thought we did enough."