The Scotsman eased through a 6-3 6-3 win over the Bulgarian to reach the quarter-finals in France.
After sealing a spot at the tournament in London for the seventh consecutive year, Murray told Sky Sports News: "It's nice. It's a great event to be involved in, it's a fun way to finish the year in London - they put on a great event there. I'm happy to have qualified."
On the prospect of ending the season in the top four world rankings, Murray said: "It would be nice. I've been asked a lot about that throughout the whole year - whether I would ever get back to the top four. I've done the first part of that and hopefully I can keep winning and keep moving up the rankings."
After today's match, the 27-year-old wrote "bad year" on the camera.