Even though he withdrew from his semi-final tie with Denis Shapovalov, Nadal's run to the last four in Paris saw him reclaim the number one spot from Novak Djokovic on Monday.
Rublev dug deep in the third set and was a break ahead but Fonseca showed incredible poise and maturity at critical moments to set up another tiebreaker.
Rafael Nadal and Novak Djokovic won their matches for their respective countries on Day 4 of the ATP Cup on Monday.
Andrey Rublev reached the final of the Qatar Open on Friday with a 7-5, 4-6, 7-6(5) win over Canada's Felix Auger-Aliassime, and will meet Jack Draper in the decider after the Briton beat Czech Jiri Lehecka.
World number one Novak Djokovic had enough on his plate already on Wednesday without marauding Russian Daniil Medvedev pummelling him to a shock 6-3, 6-3 defeat at the ATP Finals.
Madison Keys was dumped out of the Miami Open third round on Sunday, falling 6-4, 6-2 to Philippine wild card Alexandra Eala
Sumit Nagal attains career-high ATP ranking of 68
Novak Djokovic is ready to challenge Jannik Sinner and Carlos Alcaraz at the Grand Slam stage when he returns to action at the Australian Open after an underwhelming campaign this year, the 24-times champion said.
Novak Djokovic dug out a 6-7(4) 6-1 6-4 win over Czech Jakub Mensik on Friday to advance to the semi-finals of the Shanghai Masters, where he will face Taylor Fritz.
The Indian jumped six places following his runner-up finish at the Perugia ATP Challenger tournament on Sunday.
Sumit Nagal on Monday dropped out of the much-desired bracket following a string of poor show
Novak Djokovic, who has won a record nine titles at Melbourne Park including the last three, has repeatedly declined to reveal whether he has been vaccinated against COVID-19, with Australian Open organisers Tennis Australia confirming that all players would have to be vaccinated to compete in Melbourne.
Novak Djokovic's bid to add a 100th singles title to his trophy cabinet on Sunday was dashed after he was beaten 7-6(4), 6-3 by world number one Jannik Sinner in the Shanghai Masters final on Sunday.
Rohan Bopanna and Nicolas Barrientos bowed out of the Australian Open men's doubles with an opening-round loss to the Spanish team of Pedro Martinez and Jaume Munar.
Earlier this month, the ATP also announced a two-year partnership with online learning platform Coursera which will allow players to access over 4,000 courses for free.
Debutant Stefanos Tsitsipas crushed defending champion Alexander Zverev 6-3, 6-2 on Wednesday to book his place in the last four of the ATP Finals with a match to spare.
No. 2 seed Casper Ruud of Norway will take on unseeded Denis Shapovalov of Canada in the Dallas Open final on Sunday after both notched semi-final victories.
Novak Djokovic secured a semi-final place at the ATP Finals with a 6-3, 6-2 victory over Russian Andrey Rublev on Wednesday, his 50th match win of the year, while Stefanos Tsitsipas withdrew from the tournament due to an elbow injury.
World number one Rafael Nadal has been drawn alongside defending champion Alexander Zverev, Association of Tennis Professionals (ATP) reported.
Philippine wildcard Alexandra Eala pulled off the biggest win of her young career with a stunning upset of Polish world number two Iga Swiatek.
Prajnesh Gunneswaran announces retirement from professional tennis
AITA President Anil Jain, who was accused of using his position for personal gains, avoided facing a no-confidence motion from the state associations only after he agreed to step aside.
Novak Djokovic said a majority of players believe favouritism is at play in the tennis anti-doping system.
Alexander Zverev cruised past Frenchman Lucas Pouille in straight sets in the first round of the Australian Open on Sunday.
The American duo won 5-7, 6-1, 13-11 as they added the season-ending crown to the Wimbledon and US Open titles.
Dimitrov was showing signs of fatigue from his three-hour third-round match earlier in the week and could do little to stop the Spanish world number three, who next faces Argentine Francisco Cerundolo.
Djokovic helped Serbia to a 3-0 victory over Japan in their Group A opener on Wednesday at La Caja Magica where a revamped Davis Cup climax is being contested by 18 nations over seven days.
Former world number one Andy Murray is in line to play Grigor Dimitrov in the opening round of the inaugural ATP Cup, with Bulgaria qualifying among the final six teams in the nation-based tournament.
Former champion Naomi Osaka was sent packing from Indian Wells after losing in straight sets to Colombia's Camila Osorio.
Medvedev became only the fourth player in ATP history to beat the world's top three at the same tournament.
However, the 33-year-old Spaniard will not know until later on Friday whether his Herculean effort was in vain.
'I think he's bringing a fresh look to my game and I'll be able to benefit from that, no doubt, on the court. But also that champion mentality he has, I'm sure we'll match very well.'
World number two Nadal's fate will rest on his final group match against Tsitsipas.
Melbourne on Friday completed 28 days since the last reported locally-acquired case of novel coronavirus infection.
Factbox on Carlos Alcaraz, who beat Alexander Zverev
ATP events in Hamburg, Bastad, Newport, Los Cabos, Gstaad, Umag, Atlanta and Kitzbuhel will not go ahead as scheduled.
Tallon Griekspoor prevailed in a high-voltage three-set final against Benjamin Bonzi to win his maiden ATP World Tour title.
Following a victory over Alexei Popyrin at the Queen's Club Championships in his 1,000th tour-level singles contest, Murray withdrew due to the injury while trailing 4-1 in the first set of his second-round match with Jordan Thompson on Wednesday.
India's singles challenge has already ended with both Sumit Nagal and Ramkumar Ramanathan making first round exits.
Rafael Nadal's hopes of winning the year-ending ATP Finals for the first time live on after the Spaniard beat defending champion Stefanos Tsitsipas 6-4, 4-6, 6-2 on Thursday.
