Milos Raonic of Thornhill, Ont., also kept his hopes of qualifying for the season-ending tournament alive with a 7-5, 7-6 (7) win over Spain's Roberto Bautista Agut.
Following a tumultuous year that saw him change coach and recover from a serious back injury, Murray booked his spot at the season-ending tournament in London by reaching the quarterfinals at the Palais Omnisports with a 6-3, 6-3 win over No. 9 seed Dimitrov.
Before leaving the court, Murray signed "bad year" on a camera lens.
"It wasn't a jibe (at critics), it's a bit of fun," he said about his autograph. "I mean, people are going to ask me all the time why I've had such a poor year by my standards. You're allowed sometimes to say something in response to that. I don't tend to do that often, but, look, it's been a hard year, a tough year, but it hasn't been a bad year."
After missing last year's season-ending tournament following surgery on his back, the eight-seeded Scot pushed hard to qualify for the indoor event for the seventh straight year, winning three titles over the past five weeks.
Murray, who slipped from fourth in January to 12th in the rankings last month, reached the semifinals at the French Open then failed to defend its Wimbledon crown and had to wait until September to win his first title of the season at the Shenzhen Open in China.
He split with coach Ivan Lendl in March and hired Amelie Mauresmo after Roland Garros.
"It could have been a lot worse," said Murray after contesting his 22nd match in five weeks. "Coming back from surgery is not easy at all, and I learned that. The first few months of this year it was very difficult, and I had to dig deep at the end of this year in some ways to salvage the year, if you like. But it's been a good year. Not been my best year, but I would've signed up for being in this position when I had the surgery last year, I think."
The Scot was in control throughout against Dimitrov, losing only two points on his first serve as he took a measure of revenge following his loss to the Bulgarian player in the quarterfinals at the All England club this year.
Already qualified for the finals, third-seeded Stan Wawrinka failed to serve out the match before losing a 6-7 (2), 7-5, 7-6 (3) to Kevin Anderson in a match lasting nearly three hours as the hard-hitting South-African rallied to advance to the quarterfinals for the first time.
"I should have won," said Wawrinka, who has been hampered by a virus this week and coughed a lot during his press conference. "In the end, I made stupid mistakes, but I'm not panicking. I'm still Top 4 in the world and I have a Masters to play, a Davis Cup final on clay, which will be totally different from usual tournaments."
Since his quarterfinals exit at the U.S. Open, Wawrinka has won only two matches and will travel to London with his form in question. Wawrinka will also be teaming up with his Switzerland's teammate Roger Federer in the Davis Cup final against France from Nov. 21-23 in Lille.
"This year I had ups and downs that were very high or very low," added the Australian Open champion, who was two points from the match when leading 5-4, 30-0 in the decider. "But I wouldn't change anything compared to any other year of my career. I can still play well in the Masters, win the Davis Cup, and the year will be fabulous."
Anderson, who hit 18 aces against Wawrinka, will next face Tomas Berdych, who stayed on course for qualifying for the finals for the fifth straight year by beating Feliciano Lopez 7-5, 6-3. Fourth-seeded David Ferrer and No. 6 seed Kei Nishikori also kept alive their hopes of making it to London by defeating Fernando Verdasco and Jo-Wilfried Tsonga respectively.