The 36-year old skipped the French Open to focus on his grass-court season and give himself the best preparation for Wimbledon next month.
Murray, a two-time Wimbledon champion, is ranked 43rd and needs to climb around 10 positions to be seeded in SW19.
He increased those chances with a hard-fought 7-6 (1) 6-4 win over Yunchaokete, who is 130 places below Murray in the rankings.
Internet issues on the umpire’s scoring system led to a slight delay in starting the match and it took Murray a while to get going once things got under way.
As with his first round win over Chung Hyeon on Monday, Murray needed little time to hit his stride as he looked to back up his claims that he remains among the top 10 players on his favourite surface.
Chinese qualifier Yunchaokete had beaten Briton Harry Wendelken in the opening round but the step up in class left him at the mercy of Murray.
Two aces saw Murray take the third game and he broke serve in the sixth only to have Yunchaokete break back immediately, with the Briton throwing his racket to the ground in frustration.
Yunchaokete was starting to grow in confidence as he held to love to leave Murray grumbling away at the other end.
Two set points for Murray were not taken and he greeted another error with a cry of “I don’t know what is going on with my game” as the first set headed into a tie-break.
The self-administered pep-talk seemed to work as Murray dominated, this time letting out a roar of joy as he took the first set.
The outbursts of anger continued in the second set with both players still unable to put clear distance between the scores.
Murray would eventually maintain a high enough level to see off the spirited Yuchanokete and advance into the next stage as he aims to go one better than his semi-final place at Surbiton 12 months ago.