He may need a victory, or to merely win a set against the world No 2.
Tuesday's earlier action saw Britain's Joe Salisbury and American partner Rajeev Ram beat Ivan Dodig and Filip Polasek after a match tie-break to give themselves an opportunity of reaching the last four in the doubles.
The two men were now fully engaged, teasing and testing through some outstanding rallies, and Thiem had to fight off two break points for 3-3.
Thiem did not back off, though.
This looks to be a far easier contest to call on paper.
Federer broke Berrettini to open the second set, but had to overcome a slight wobble at 4-3.
Djokovic appeared set to consider regulate following breaking on Thiem's next assistance video game, but the Austrian returned the favour to draw stage at three-3.
It's official! A 'Friends' reunion is on!
According to reports, Bob Greenblatt, WarnerMedia's Entertainment Chairman, has been the biggest advocate for the reunion . Several sources say that the stars and the creators of the comedy ( David Crane and Marta Kauffman ) from Warner Bros.
Met Office warns of heavy rain for Stamford area
The weather experts predict that Ireland could be hit by sleet and show, with wintry falls hitting the higher ground by Wednesday. This warning is in place from midnight until 11.45pm with forecasters warning that up to 60mm of rain could fall in some places.
Nikki Haley on Ukraine: ‘Hard to See Where Impeachment Would Qualify’
In her book, Haley retells the story of the president's reaction to the violence in Charlottesville after the tiki-torch parade. Others have claimed that she is trying to replace Vice President Mike Pence as Trump's running mate.
But the Serb was not about to let this slip. I had a bit of luck here and there.
Could Thiem stay mentally resilient in the face of such a test and such a prize? He was serving for the match. It would take another tie-break.
Thiem is 2-0 after wins over Federer and Djokovic, and Berrettini is out of contention at 0-2. But he went for broke, and two winners got him the lead.
Thiem has delighted the crowds here with his ambitious, big-time tennis-surely bolstered by his enthusiastic coach Nicolas Massu this season-and by his quietly-spoken charm. The victor goes through, the loser is left to go back home, and whichever way you look at it, it's interesting to note that one of Federer or Djokovic won't be playing in the semifinals of the ATP Finals. "I think it's going to be helpful for also the rest of the players".
"I'm happy just being pain free, healthy and love what I'm doing".
"I thought he deserved to win".
"He just played very courageous tennis ... He went for broke". What's even more stunning is his record against Federer and Djokovic in the last eight matches he's played against them - an unbelievably awesome 7-1.
"Actually, it's good for me to play him again, and maybe that all helps to get a chance to get him back", Federer said.
It means only the victor of Thursday's match between Djokovic and Federer, who have 11 ATP Finals titles between them, will still be in London over the weekend. Federer has won the title six times but, remarkably, not since he beat Jo-Wilfried Tsonga in 2011.