Warren defeated world number 12 JB Holmes in his opening group match on Wednesday and knew victory over Brooks Koepka on Thursday, coupled with Holmes beating Russell Henley, would see him effectively advance with a game to spare.
The 34-year-old from Glasgow was doing everything possible to fulfil his side of the bargain, taking advantage of some sloppy play from Koepka to move three up at the turn.
Koepka ran up double bogeys on the second and third and, although the big-hitting American twice cut his deficit in half either side of a Warren birdie on the fifth, Warren birdied the eighth and was conceded the ninth when Koepka found more trouble.
Holmes and Henley were all square after 11 holes with Henley twice taking the lead before carding a double-bogey on the 10th.
England’s Paul Casey was also seeking his second win after needing 22 holes to get the better of Chris Kirk, the former Volvo World Match Play champion taking an early lead against an off-form Adam Scott, who was comprehensively beaten by Francesco Molinari on Wednesday.
Molinari was two up after four on Kirk to raise the possibility of a Friday showdown between the European duo, with the winner moving into the last 16 on Saturday morning.
World number one Rory McIlroy had only needed to be an approximate one under to ease past Jason Dufner in his opening match and repeated his birdie on the par-five first to take the lead against Brandt Snedeker.
Koepka closed the gap with a birdie on the 12th, but Warren responded with his own birdie on the 15th to move three up with three to play.
However, Henley had taken the lead with a birdie on the same hole after Holmes had seen his approach hit the flag and spin away from the hole.
McIlroy had moved two up on Snedeker with a birdie on the eighth, while Billy Horschel was one up on Jason Dufner after seven to remain on track for a winner-takes-all clash with McIlroy on Friday.