Second seed Joachim Johansson, however, retired with a fever from his quarter-final against his Swedish compatriot Michael Ryderstedt.
Johansson won the first set 6-3 but withdrew when Ryderstedt broke him to 5-3 in the second.
Verdasco, untroubled by the crowd's support for the American, matched Agassi in the opening set as both dominated with their service.
Johansson beats Agassi in Stockholm
"He's tough for anyone to play," said Agassi.
"He's left-handed with a very big serve. It's a difficult serve to read and to return and then he has a very big forehand, so if you just get it in play and you give him the chance to hit the forehand, the point is finished."
Verdasco, specialising in aces, needed only to fight off one break point on the way to the tiebreak but failed to sustain his excellence as top seed Agassi broke him in the tiebreak to 5-4 before serving out.
In the following set Agassi started to read Verdasco's serve, breaking the Spaniard to 2-0 and again to 6-2 to seal the match.
"In a tiebreaker you get a little lucky or you get a little unlucky...but in the second set I started to get more returns in and to play more from the baseline and I felt very comfortable then.
"I played a good first game to break him, and then once I was in the lead I think it was a big difference."
The Las Vegan next faces fourth seed Tommy Haas, who defeated Belgian Olivier Rochus 6-3 7-6. Both Haas and Agassi have yet to lose a set.
"We played twice this summer, back-to-back in Los Angeles and in Canada in Toronto, one and one, we played three sets both times. So it's always a difficult match," said Agassi of Germany's former world number two.
"Tommy is in my opinion one of the best players in the world, he should be up at the top."
Taking on another Swede in the semis, Ryderstedt faces 2002 Australian Open champion Thomas Johansson, who overcame a foot injury to beat Romanian third seed Andre Pavel 7-6 7-5.
Agassi keeps Masters Cup berth in view
Former world No.2 Norman retires