In his opening match, Dimitrov needed three sets to advance past fourth seed Dominic Thiem of Austria, but against Busta and fellow semifinalist David Goffin of Belgium, Dimitrov lost only four games in four sets.
Dimitrov, playing the season finale for the first time, joins Group Boris Becker victor Roger Federer as the only unbeaten singles players, and the Bulgarian will fight for the champion berth against American Jack Sock on Saturday.
In a fluctuating see-saw battle, world No 3 Zverev dug deep with his never-say-die attitude coming to the fore, as he slowly reeled Sock back in to level at 4-4. He played really well in the second - he served really well and dictated the points.
A bruising first set went in Sock's favour before Zverev took the second easily.
"That was a roller coaster match, for sure", Sock said.
Jack Sock joined Boris Becker group victor Roger Federer in the semi-finals of the ATP Finals on Thursday, after upsetting Alexander Zverev in a thriller. I started doing that midway through the second set. I'm looking forward to playing Goffin or Thiem'. You never know what can happen.
"I was telling myself try to relax a little bit, there's so much pressure on every match in the season because if you lose you go home", Federer said in his on-court interview after the game.
While Sock played with a smile and on his face and some sparkle on his racket strings to reach this weekend's last four of the ATP Finals, Thiem has lacked inspiration. A lot of chances in the first set but Marin served well and was a bit better in the breaker. Goffin pulls one back on a Federer unforced error, but he follows with a missed forehand down the line and Federer has another break-point chance, this one a set point.
The season-ending extravaganza ATP Finals ends another memorable year which will be covered via our website www.skysports.com/tennis with live blogs, reports, reaction and expert analysis as the season reaches its climax.
Goffin: "I've never found a key to beat Roger".