After losing the first set to Taro Daniel, Murray battled back to win 1-6 6-2 6-4 for what was his 700th on the ATP Tour.
It was a milestone Murray has had his eye on for some time, and now that’s been ticked off he is already targeting the next goal on his list.
“It means a lot,” Murray told BBC Sport after the win.
“I didn’t have goals like that, even four or five years ago, but obviously after what’s happened these last few years these are like small milestones.
“At the end of last year my goal was to try and reach 800 match wins, but first things first, let’s try and get to 700.
“In my best years I was winning 65-80 matches, so if I was winning 40-50 matches for the next couple of years, it’s certainly doable. I think I’m on nine wins this year and I’m not really playing that well.”
Murray’s attention will now turn to Bublik, as he looks to win two matches a tournament for the first time since the Sydney International at the start of the year.
Date, venue and UK start time
The round of 64 match between Andy Murray and Alexander Bublik will take place on Sunday, March 13.
The time will be confirmed later on Saturday evening when the order of play is revealed.
Jordan Thompson or Grigor Dimitrov await the winner in the next round.
How to watch Andy Murray vs Alexander Bublik
TV channel: The match will be broadcast on the Amazon Prime streaming service.
Live stream: Amazon Prime subscribers will be able to watch the match either on their website or through the app.
Andy Murray vs Alexander Bublik head-to-head record
The pair met last month in Rotterdam, when Murray came out on top with a 7-6 6-4 win in the first round.
Murray wins: 2
Bublik wins: 0