Woods spent just 10 minutes on the course Saturday morning, completing his rain-disrupted second round and missing the cut.
Among the players who turned around to start the third round, Beem was red-hot. He birdied the 17th hole and parred the last in a nine-under 63 on the Magnolia course that included nine birdies.
The 2002 PGA champion's 19-under total of 197 was one stroke ahead of six players, including in the clubhouse Mark Wilson (63) and Mark Calcavecchia (65).
The other four players a shot back - South African Tim Clark, Sweden's Carl Pettersson, Tom Pernice and Australian Geoff Ogilvy - were among 25 players unable to complete the round due to a late afternoon thunderstorm.
Pettersson was the halfway leader, completing an 11-under 61 on Saturday morning for a two-stroke lead over Pernice after two rounds.
Play was to resume Sunday with the final round to follow.
Woods had no success when he returned from a weather disrupted round on Saturday.
Needing two birdies to make the cut, Woods promptly bogeyed 17 and parred the last to complete a one-over 73 on the Magnolia course.
That left him at three-under 141, three strokes shy of the cut, which was at six-under 138.
"I played terrible," said Woods, a two-time winner of this event. "I hit it all over the place. These fairways are about 300 yards wide, but when you're missing it both ways, you can't aim it."
Woods had missed just two cuts his entire career, at the 1997 Canadian Open and this year's Byron Nelson Championship, and he also withdrew from the 1998 Pebble Beach National Pro-Am.
His missed cut at the Byron Nelson in May ended a record streak of 142 successive events in the money, a feat that impressed some of his peers even more than his 10 major championship.