The shocking setback for McIlroy extended a disappointing start to the year for a player expected to become one of the sport's dominant figures. He missed the cut in his only other appearance of the season.
The opening round began on Wednesday, but was suspended due to a heavy snowfall. The second round will be played Thursday and the third round will get underway.
Among Thursday's surprises were a 1-up victory for PGA Tour rookie Russell Henley over former Masters champion Charl Schwartzel, Alexander Noren's 6-and-4 demolition of Dustin Johnson and the 1-up win for Richard Sterne over Jason Dufner.
Lowry chipped in for birdies at both the 11th and 12th holes of his match with McIlroy and then took a 2-up lead at the par-5 13th with an eagle. McIlroy also suffered three bogeys and a double bogey during the match.
The Woods-Howell confrontation was all square with four holes to play, but Howell birdied both the 15th and 16th to seize the advantage.