Murray dismissed Madrid man Verdasco 7-5 6-4 in mostly impressive form, vindicating his top seed status at Queen’s Club as other big names tumbled.
The 28-year-old would become the eighth man to win a record four Queen’s titles with victory this year, and reigning champion Grigor Dimitrov’s second-round exit further improved those chances.
Second seed Stan Wawrinka has already fallen by the wayside, and Dimitrov surrendered his crown with a lacklustre straight-sets defeat to Gilles Muller.
Luxembourg’s Muller will now meet Murray in the quarter-finals, with his British coach Jamie Delgado sure to relish the match-up against his friend and compatriot.
Murray is the only star at Queen’s to hit top gear so far this week, and had few issues overall moving past Verdasco, save dropping a service game in the first set.
Spaniard Verdasco came closest to derailing Murray’s 2013 Wimbledon title charge in a tense quarter-final before the Dunblane native rallied for a five-set victory.
Murray had no such problems on this occasion, breezing through to the last eight with purpose, poise and confidence.
World number 42 Verdasco still had more than enough quality to provide a tangible test for Murray, still fresh from his best-ever clay-court campaign.
The 2012 Olympic champion was pegged back after an early break in the first set, only to break again and take control.
Murray saved a break point at the start of the second set, before staving off three more in his next service game to stay on course.
The set stayed on serve until Murray led 5-4, breaking Verdasco’s serve to convert his second match point.