Celtic have yet to pick up a league point in Dundee this season.
In October, they lost at Dens Park for the first time since 1988, while Dundee United beat them for a second time at Tannadice last time out.
That took the champions’ league defeats to eight, double last term’s total and five more than the campaign before.
By the time Celtic kick off (16:30 BST), Rangers will have hosted Dundee United on Saturday (15:00) and Hearts will have played their game away to Livingston earlier on Sunday (14:00).
“Psychologically, there’s an advantage to playing early if you go and get your results,” O’Neill said. “If you don’t, it opens the way for you.
“I’m hoping that between now and the end of the season, it might work in reverse.
“You just have to try and take care of your own game that you are supposedly in control of.”
O’Neill gave an update on injured players Arne Engels and Julian Araujo.
“It’s a thigh,” O’Neill said of right-back Araujo, who has returned to parent club Bournemouth for treatment. “He’s doing fine in recovery, now. We expect to see him back, hopefully in the not too distant future.
“Arne’s come back now. We’ll see. Each day it’s a good day for him, he’s trained most of the week. We’ll just keep any eye on things at this minute. We couldn’t rule him out or in for Sunday.”