Murray, who reached the semi-finals here last year where he lost to eventual winner Rafa Nadal, served well and never gave his Japanese opponent a chance.
As Ito tired, Murray won the fifth game of the final set to love then produced a winning serve to seal the sixth game and finish the match in one hour 35 minutes.
Murray has had a hit-and-miss claycourt season so far, troubled by a back problem and inconsistent form, but he was composed and clinical against the world number 68.
The Scot started off by breaking Ito's first service game, following with a hold and a second break. The 24-year-old hardcourt specialist from Japan did hold once but, after saving three set points, misplaced a backhand to hand Murray the opener.
The second set was a more even affair as Ito played some ferocious groundstrokes, breaking Murray back at 2-2.
He had three more break points later on but Murray held on before breaking once more at 5-5, initially losing three break points but winning it off deuce as Ito hit a forehand long.
The final set was far more straightforward as Ito wilted, making countless errors as Murray closed out the dreaded bagel.
The Scot, who was watched by coach Ivan Lendl, will play Finn
The Finn went through after