Despite some wayward hitting from Verdasco during the opening set, the Spaniard managed to save two break points before breaking Murray to take it 6-4.
Murray looked to have steadied himself during the second as he established a 3-1 lead, but Verdasco battled back to win the next five games in a row on his way to closing out the set 6-3.
While the world number two appeared edgy during the previous 80 minutes, he stormed back in the third set and went on to claim it 6-1.
A nervy fourth set saw Murray save two break points with Verdasco leading 3-2, and the Brit then dug in to break again as he came through 6-4.
The fifth set saw momentum swing both ways as each player managed to hold on to their own serve fairly comfortably, with the first break point coming Murray's way in the 11th game. The Scot took full advantage to move into a 6-5 lead.
He then finally completed his comeback by serving out the match, claiming the last set 7-5 to book his place in the semi-finals of Wimbledon.