The 13th-seeded Murray never allowed the Russian to establish a comfortable rhythm and served and returned efficiently.
"It was about playing the big points better than the guy who's No. 4 in the world," Murray told reporters.
"I had some big serves in the last game when I needed to, and after a pretty bad start, I came back well."
After winning the tiebreaker 7-3 after an ace, service winner and forehand unforced error from Davydenko, Murray never looked back, breaking the Russian in the opening game of the second set.
Murray won the contest with a 136-mph ace.
"He surprised me a bit
"I just had to try to hang in, maybe sliced a little bit too often in the first set and started hitting over my backhand. It's really hard to get someone like him out of his rhythm."
Murray is off to a roaring start this season, posting an 18-3 record, winning his second career title in San Jose and reaching the Doha final.
The 19-year-old Scot will meet the winner of the match between fifth seed Fernando Gonzalez of Chile and ninth seeded German Tommy Haas in the quarter-finals.
Number 12 Novak Djokovic of Serbia also reached the quarter-finals, beating Julien Benneteau of France 6-3, 6-1.
The Serbian will play either David Ferrer or Carlos Moya.