The Wimbledon champion, competing for the first time since splitting with coach Ivan Lendl, found himself in trouble early on in the match as Ebden secured a break of serve in the second game.
Ebden was forced to battle to stay a break ahead at 3-1 but he managed to frustrate Murray on his way to a 6-3 success in the opener.
Murray produced an impressive response at the start of the second set to pile the pressure on his unseeded opponent and the British number one continued to find his range to cruise to a 6-0 win in under 30 minutes.
The sixth seed's confidence improved with the scores level at 1-1 and only a sloppy service game prevented him from whitewashing his rival in the third set.
However, Murray's frustration was short-lived as he comfortably dictated the flow of the contest in the closing stages to win the third set 6-1 and book his spot in the next round.