With four matches a day -- three singles and a doubles, the players can earn a point for each win on Friday, two on Saturday and three on Sunday.
Rafael Nadal and Roger Federer won their third round matches to move closer to a blockbuster semi-final clash at the US Open.
The field of newbies, who compete on Sunday for the first four spots in the US Open quarterfinals, is as eclectic as they come.
Svitolina held off 42nd-ranked Czech Katerina Siniakova 6-0, 6-7 (5/7), 6-3 while Thiem finished off Australian Alex de Minaur 6-4, 6-1, 6-1 under sunny skies.
It was in the eighth game of the second set that the 22-year-old served an ace to finish the match.
Dominic Thiem demolished defending champion Novak Djokovic 7-6, (7/5), 6-3, 6-0.
Novak Djokovic overcame having to play twice in a day before cruising into his eighth final of the Rome Masters with a ruthless 6-1, 6-0 win over Dominic Thiem on Saturday.
Novak Djokovic will now face Dominic Thiem after the Austrian starlet sent seven-time champion Rafael Nadal of Spain crashing out in the quarters.
Nadal, a former seven-time champion in the Italian capital, had dominated Thiem to win the Madrid Masters final last week.
The Spaniard is now 15-0 on his favoured surface this year having also picked up his 10th titles in Monte Carlo and Barcelona in recent weeks.
Rafael Nadal celebrated his victory in Barcelona in a traditional manner.
Rafael Nadal won in Barcelona between 2005-2009, 2011-13 and now in the last two years.
Rafael Nadal gets the better of Argentina's Horacio Zeballos while Dominic Thiem stuns Andy Murray in the semis of the Barcelona Open
Dominic Thiem lost his opening group stage match against Novak Djokovic, but the ATP Tour Finals debutant could still make the last four after seeing off flamboyant Frenchman Gael Monfils at London's O2 Arena
Novak Djokovic responded to losing the first set against Dominic Thiem by angrily hitting a ball into the court and it bounced towards the spectators before disappearing into a staircase
Dominic Thiem blasted 47 winners, 20 in the last set, on his way to a 1-6, 6-4, 6-4, 7-5 victory over Pablo Carreno Busta. In women's singles, fifth-seed Simona Halep defeated Timea Babos 6-1, 2-6, 6-4 to advance to Round 4 of 2016 US Open
Novak Djokovic's path to the gold has already been eased by the withdrawals of top 10 players Roger Federer, Stan Wawrinka, Milos Raonic, Tomas Berdych and Dominic Thiem
Roger Federer, who is returning from a back injury that ruled him out of the French Open, saw his preparations for Wimbledon unravel as Dominic Thiem battled through 3-6, 7-6 (9/7), 6-4