The Briton beat the Chinese Taipei player 6-3 6-3 7-5 on court one this afternoon, facing break points in just one game.
The second seed will play Spain's Tommy Robredo in the next round.
Read how all the action unfolded below.
3.52pmGood afternoon. Andy Murray will be heading out to court one at Wimbledon in the next few minutes to face Lu Yen-Hsun in the second round of Wimbledon.
3.53pmThe duo have played twice before, each taking one win. Murray beat Lu at Indian Wells earlier this year, while the Taiwanese player beat the Brit at the Olympics in 2008.
3.56pmThe world number 73 has only progressed past the third round of a Grand Slam once in his career, but it was at Wimbledon. He made the last eight in 2010, where he was eventually beaten by Novak Djokovic.
3.58pmThe players have just come onto the court. Unsurprisingly, the crowd give a big cheer to the British number one. On paper, this should be a fairly straightforward encounter for the US Open champion, but Lu has nothing to lose, and showed impressive tenacity in his lengthy match with James Ward on Monday.
4pmMurray's section of the draw has already lost one of its highest-ranked players today, following Marin Cilic's decision to withdraw from the tournament with a shoulder injury. The Croatian was seeded to face Murray in the fourth round.
4.03pmIf you want to keep up with some of the other matches taking place at Wimbledon this afternoon, you can currently follow live updates from Jo-Wilfried Tsonga's match against Ernests Gulbis, and Maria Sharapova's clash with Michelle Larcher de Brito with Sports Mole.
4.05pmSome members of the crowd have really made an effort this afternoon. There are two men sat just behind Murray's chair dressed as Superman!
4.05pmRight then, play is just about to get underway, with the Brit serving first.
Murray 1-0* LuIt's a slick start from Murray. Lu is unable to return the opening serve, before the second seed slices a backhand past his opponent. He wraps the game up with an ace followed by a forehand winner.
Murray *1-1 LuLu takes the opening point of the game after getting the better of Murray in a long rally, and secures a 30-0 lead with a brilliant overhead smash. Lu continues to play some solid shots from the baseline, and seals the game when Murray hits his backhand to the net. It's a good start for the player from Chinese Taipei.
Murray 2-1* LuMurray deceives Lu with a high lob to take a 40-0 lead, before a series of forehands from the baseline force an error from Lu. The 29-year-old has made an energetic start to the match, but he doesn't seem to be able to match Murray's strong ground strokes, and has looked uncomfortable returning his serve.
Murray *2-2 LuLu forces Murray to cover a lot of ground as he controls the rally from the back of court before wrong-footing the Briton with a volley. After a couple of good forehands, he finishes the game with his first ace of the match.
Murray 3-2* LuMurray loses his first point on serve when Lu's shot strikes the net chord. The Scot keeps his cool to take the next point, but Lu makes a superb smash from behind the baseline, and follows it up with a stunning cross-court forehand to bring up break point. However, he puts too much power on his return on the next shot, and smashes it into the upright on the net. At deuce, Lu manages to find the baseline with a forehand, wrong-footing Murray to give himself another chance to break, but a big serve from the world number two saves it. An ace gives Murray advantage, and he makes to get the hold with another big serve, which Lu returns long. That was a tricky game for Murray, and he'll be relieved to have come through it.
4.27pmLu has looked dangerous when he gets into a rally with Murray, and has been moving around the court with impressive speed early in this contest.
Murray *4-2 LuBREAK! Lu struggles with his ball toss early in the game, causing him to miss a couple of first serves, before he fires a forehand into the net. The Taiwan player does have an unusually high ball toss. A wide forehand gives Murray two chances to take the break, but he needs just one, as Lu finds the net again.
Murray 5-2* LuDropping his serve seems to have knocked Lu's confidence, as he makes two poor returns, before an ace takes Murray to 40-0. A mistake from the Brit keeps his opponent in the game a little longer, but another long return ensures a comfortable hold for Murray, who has now won three games in a row.
Murray *5-3 LuLu manages to save two set points to take his first game in four. A couple of poor serves give Murray a chance to take the game, but he misses two returns to take the game to deuce. The Scot has one of his infamous rants at himself, but it doesn't work, and he'll now try to serve for the set.
4.39pmSET! Murray 6-3 Lu
4.41pmAfter a wide shot at the start of the game, Murray finds some brilliant serves to make returning impossible for his opponent, wrapping up the opening set in 33 minutes.
Murray 6-3 *1-0 LuBREAK! A sliced backhand gives Murray the opening point of the second set, but he finds the net with a forehand on the next rally. Once again, Lu struggles with his ball toss, resulting in the first double fault of the match. Murray brings up break point when Lu fires his forehand long, and he takes the game when the Chinese Taipei player makes the same mistake on the next point.
Murray 6-3 2-0* LuMurray finally seems to be getting the better of Lu during rallies, with the 29-year-old struggling the get the length of his strikes right. At 40-15, the Scot smashes another ace past his opponent to take the game.
Murray 6-3 *2-1 LuLu manages his best service game since early in the first set, managing to get a bit of extra pace on the ball to make returning difficult for Murray.
4.52pmSome breaking news from centre court, Jo-Wilfried Tsonga has retired from his second-round match with a knee injury. The Frenchman had been seeded to meet Murray in the quarter-finals.
Murray 6-3 3-1* LuMurray makes a strong start to the game, quickly taking a 40-0 lead, but a double fault causes him to lose his rhythm, and Lu think he's taken the game to deuce. However, Murray challenges a call on the sideline, where Lu had landed a forehand winner, but hawkeye reveals that it was a fraction wide, giving the US Open champion the game.
Murray 6-3 *3-2 LuLu is on the back foot early on, as Murray gets a superb lob past his opponent. The Taiwan player tries to force a backhand winner, but slices it too wide to give Murray two break points. The Brit wastes the first with a wide forehand, but Lu volley to bring up deuce. A poor return from Murray gives Lu advantage, and he's able to hold serve by catching the Scot out with a drop shot.
Murray 6-3 4-2* LuMurray claims the opening point with a rare volley, before beating Lu in a baseline rally. A well-timed forehand gives Murray a 40-0 lead before another volley seals the game. Murray is using a wide range of shots this afternoon.
Murray 6-3 *4-3 LuSome big serves from Lu force Murray to make a couple of long returns, before he smashes a forehand shot into the net. However, two short efforts from Lu allow Murray back into the game, but he holds with a drop shot.
Murray 6-3 5-3* LuMurray dictates the play from the baseline. Lu's early pace around the court seems to have disappeared, probably not helped by his lengthy encounter with Ward on Monday. Lu comes into the net to volley, but Murray gets the ball back down the sideline to wrap up the game, and needs just one more to take a two-set lead.
5.14pmSET! Murray 6-3 6-3 Lu
5.15pmWhat a miserable end to the second set for Lu! Murray made some brilliant shots from the back of court early in the game to bring up a couple of break points, but Lu was able to save them both. However, a double fault from the 29-year-old handed the Scot a two-set lead.
Murray 6-3 6-3 1-0* LuWell it's not the easiest hold for Murray, but Lu never really looked like braking. The pair shared the opening four points of the game, with Lu making some strong returns, but a sloppy forehand found the net to give Murray the game.
Murray 6-3 6-3 *1-1 LuLu looks extremely focused at the start of the game, finding some brilliant serves to help him to a 40-0 lead. However, he then misses two first serves in a row to let Murray back into the game. Murray mis-hits a shot, which flies high, and Lu manages to smash it back past Murray to complete the game.
Murray 6-3 6-3 2-1* LuLu attacks the Murray serve early in the game, forcing the Brit to smash his forehand into the net. However, the second seed makes two aces in a row to clinch the game.
Murray 6-3 6-3 *2-2 LuOnce again, Lu seems to be having problems finding an accurate ball toss, but it doesn't seem to affect him too much, as Murray makes several long returns to give Lu a 40-0 lead. He keeps the game alive with a superb lob to the baseline, before making a solid volley, but another long effort from the Briton ensures that the third set remains on serve for now.
Murray 6-3 6-3 3-2* LuMurray comes into the court in from the baseline to take the first two points, before Lu returns the ball to the net. The Taiwan player manages to pick out the sideline with a brilliant forehand, but Murray wraps up the game with a big serve, which Lu can't return.
Murray 6-3 6-3 *3-3 LuLu's serve has been up and down throughout the match, but this game was definitely not one of better ones. The 29-year-old struggles to get his first serves in, relying on a fairly safe but slow second serve. The errors make it easy for Murray to attack, and he brings up a break point, but Lu gets a lucky hit on the net chord to bring up deuce. Both players claimed advantage several times, but it was Lu who managed to convert, catching Murray out with a brilliant drop shot.
Murray 6-3 6-3 4-3* LuBuoyed from holding serve after a difficult game, Lu goes on the attack, but Murray manages to land a tricky forehand effort on the baseline, frustrating his opponent. A couple of big serves help him hold serve again.
Murray 6-3 6-3 *4-4 LuLu makes a good start, claiming the first two points of the game with some brilliant smashes. However, the troublesome ball toss plagues him again, forcing another double fault. Lu regains his composure and seals the game with a strong forehand down the sideline.
Murray 6-3 6-3 5-4* LuMurray hasn't volleyed much during this match, but he does in the opening point of the game, following it up with a drop shot in the next rally to claim a 30-0 advantage. The Scot mis-reads a forehand from his opponent, but a good forehand shot of his own followed by an ace round up the game for Murray. Lu must hold serve next to keep himself in the match.
5.59pmA long forehand from Lu gives Murray a match point.
5.59pmA strong serve from the Taiwan player saves the point and brings up deuce.
Murray 6-3 6-3 *5-5 LuA wide forehand gives Murray the match point, but a superb serve from Lu forces a poor return from the Brit. Lu gains advantage when Murray fires another return long, and a good forehand ensures that he holds serve again and keeps the match alive.
Murray 6-3 6-3 6-5* LuThe frustration of the missed match point results in some huge serves from Murray, as Lu fails to get any returns in, giving the Brit what has probably been the easiest and quickest hold of the match so far.
6.05pmMurray has two match points.
6.06pmGAME, SET & MATCH! Murray 6-3 6-3 7-5 Lu
6.08pmLu manages to save the first break point with a brilliant smash from close into the net, but Murray engages him in a rally and forces the 29-year-old to fire his forehand just long, allowing Murray to progress to the third round in straight sets.
6.09pmThe autograph hunters are keeping Murray on court, one even seems to be asking him to sign a bottle of wine! The second seed will face Spain's Tommy Robredo in the next round, following his win over Nicolas Mahut earlier this afternoon.
6.11pmFollowing his victory, Murray said: "I thought I kept my concentration well on serve, I served very well throughout the match. Each game i was putting a lot of pressure on his service games, he came out with some great shots."
6.12pmOn his next opponent, Murray said: "He's started playing some really good tennis. He's very, very fit, he works incredibly hard, serves solid, good forehand. It's going to be a really tough match."
6.15pmWell that's all from this match, but you can follow live coverage of Roger Federer's match against Sergiy Stakhovsky. Thanks for joining me this afternoon, good bye.