McIlroy beat Brandt Snedeker 2up, while Spieth downed Matt Every 4&3 to force their respective groups into must-win matches on Friday.
It was a relatively comfortable day at the office for McIlroy who never trailed against Snedeker and held a two-stroke advantage after 10 holes. However, Snedeker squared matters with birdies at the 11th and 12th, only for McIlroy to respond with birdies of his own at the 15th and 18th.
It was plain sailing for Spieth who registered six birdies in seven holes from the sixth to the 13th to quell an early charge from Every.
World number one McIlroy will now face Billy Horschel on Friday, with the pair tied at the top of Group 1 with two wins apiece. Masters champion Spieth finds himself in the same situation in Group 2 where he will face off against Lee Westwood for a spot in the last 16.
There is another mouth-watering showdown on the cards in Group 4 where Bubba Watson will face South African Louis Oosthuizen, the man he defeated in a play-off at the 2012 Masters.
Earlier in the day, Rickie Folwer and John Senden booked their places in the last 16 with wins over Shane Lowry and Bill Haas respectively.
Henrik Stenson, Adam Scott, Jason Day, Keegan Bradley, Graeme McDowell, Jason Dufner, Jimmy Walker and Ian Poulter are among those who saw their chances of progressing ended on Thursday.