The world No 1 made only one birdie to halve the first, but he was then content to grind out the pars as Dufner made a string of mistakes to gift McIlroy a comfortable 5&4 win.
The new round-robin group format at TPC Harding Park in San Francisco spared Dufner an early flight home, while McIlroy will expect tougher tests against Group 1 rivals Brandt Snedeker on Thursday and reigning FedExCup champion Billy Horschel on Friday.
Masters champion Jordan Spieth seemed to like the course in his convincing 4&2 win over Mikko Ilonen.
Spieth reeled off three birdies in four holes from the fifth, but Ilonen hit back with birdies at nine and 11 to reduce the deficit to one before the young Texan won the next two holes and wrapped up victory on the 16th.
Third seed Henrik Stenson paid the price for missing a four-foot putt for the match on 17 as he slipped to defeat to John Senden at the first extra hole.
Justin Rose also suffered a surprise 3&2 loss to Marc Leishman in the opening match of the tournament, while defending champion and world No 7 Jason Day crashed to a 4&3 defeat to Charley Hoffman.
Jimmy Walker was edged out by compatriot Gary Woodland at the 19th, while Francesco Molinari pulled off one of the biggest wins of his career as he cruised to a 5&4 win over Adam Scott.
Ben Martin provided the highlight of the first day, firing a superb hole-in-one at the 230-yard 17th before closing out a 1up victory over 14th seed Matt Kuchar.