In the dramatic scene when Michael exclaims, "Pentangeli is alive!", Tom concludes, "Roth played this one beautifully."

How did Tom know Roth was behind the perjury trap? Based on that scene alone, I'd have thought that the trap was laid by the FBI acting in concert with the Senate subcommittee chairman. They had ample motivation to trap Michael. It isn't until later, when Michael is alone with Fredo, that Fredo tells him, "The Senate lawyer, Questadt, belongs to Roth." I don't think Michael knew that until then.

Your thoughts?

TB, probably just by default. He couldn't figure that the FBI would do it.

I also don't understand how "Roth played it beautifully" because Pentangeli being alive was a stroke of luck because the Rosato Bros. failed in killing him. Roth wanted him dead.

He knew Frankie was garroted at the Rosato Brothers meeting, and he knew Michael didn't give the order to kill him. That he was kept alive in secret had to have been engineered by Roth, hence the "played it beautifully" line.