Graeme McDowell managed to complete his round, hitting a three under par 68 to reach one under par for the tournament.
Rodgers, who reached 11 under after four straight birdies, had just three holes left in the second round when the horn blew, having been seven under through 15 on Friday.
Fowler, 28, was dialed in early, knocking his approach inside five feet at the par-4 third and converting for birdie, then adding another birdie at the par-5 fifth. John Huh, the 2012 tournament victor, also carded a 67.
Rickie Fowler sat one shot off the lead when play was suspended due to darkness during the second round of the OHL Classic at Mayakoba.
First-round leader Patton Kizzire sits alongside Fowler on -10 after he followed up his career best round of 62 at the El Camaleon Golf Club on Thursday with a 70.
Kizzire's late rally snatched the clubhouse lead from Brian Gay (65) and Brandon Harkins (68), while Martin Piller raced to eight under after he birdied his first four holes of the day.
Kizzire finished the second round with a 70.
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