Toms was at 8 under Friday when the round was stopped because of severe thunderstorms. He birdied two of the five holes he played Saturday morning.
Perry had finished his round when the rains came Friday, following up an opening round 61 with a 68 to go 11 under par.
Ben Curtis also made a strong move Saturday, finishing a second-round best 64 to move into a tie for fifth place.
The tournaments third round was scheduled to start before noon.