Chardy saved six set points before being taken do a decider by Barrere, who passed up six chances to break his opponent and succumbed to a 6-3 3-6 6-3 defeat.
Seventh seed Adrian Mannarino exited after a 6-3 6-4 loss to Alexander Bublik, while Filip Krajinovic – seeded sixth – came from a set down to beat Kyle Edmund 4-6 6-3 6-3.
There were also wins for Fernando Verdasco, Aljaz Bedene, Corentin Moutet and Miomir Kecmanovic.
The British number one has enjoyed an unbeaten week at the LTA's National Tennis Centre, including beating Andy Murray in Saturday's semi-final, and was in fine form on Sunday.
Edmund was broken three times during a first set in which Evans' power from the baseline and ability to move forward was the difference maker.
It was a great start to the second set for Edmund, who broke at the first time of asking, only to hand that advantage straight back.
The clinical Evans then won four straight games from 2-2 to wrap up the win in one hour and 18 minutes.
"As Kyle said it was like a tour event and I wasn't sure how it would work out," Evans said.
"Thanks to everyone who has worked on it, all the players have loved it - that's the truth. Everyone has been raving about the tournament.
"It has been a long week and a great week."
Murray was scheduled to play in the third-place match but withdrew due to a shin injury.
His replacement, James Ward, was beaten 6-3 7-5 by Cameron Norrie.
Djokovic – who saw a three-year visa ban lifted in November – played with Vasek Pospisil in the doubles on Monday, but this was his first singles outing in the country since his vaccine-related absence from last year's Australian Open.
"For the first match [of the season] I can't complain," Djokovic said. "I played very well. I thought the first six games were very competitive and I have never faced him before.
"But once I made that break at 3-2 in the first set I thought I stepped it up and played really good tennis for the rest of the match."
Elsewhere in Adelaide, third seed Daniil Medvedev advanced after Lorenzo Sonego retired hurt with the Russian leading by a set, while sixth seed Jannik Sinner eased past Kyle Edmund 6-3 6-2.
Seventh seed Denis Shapovalov is also through after coming from a set down to beat Rinky Hijikata, but fourth seed Andrey Rublev is out after losing to Roberto Bautista Agut in three sets.
The Spaniard will face Sebastian Korda next after he beat Andy Murray 7-6 (7-3) 6-3, while eighth seed Karen Khachanov advanced after beating Pedro Cachin 6-2 6-4.
At the Maharashtra Open in Pune, Aslan Karatsev had no problems seeing off Pablo Andujar 6-1 6-3, with the eighth seed set to face Tim van Rijthoven in the last 16 after the Dutchman beat Radu Albot 6-4 6-4.
There were also wins for Maximilian Marterer against Elias Ymer and Pedro Martinez against Ramkumar Ramanathan.
Edmund – the eighth seed – defeated Japanese opponent Yasutaka Uchiyama 7-5 6-4 at the ATP Tour 250 tournament on Tuesday.
The Brit won 86 per cent of his first serves as he earned a clash with Dominik Koepfer after one hour, 44 minutes.
German Koepfer defeated last year's runner-up Brayden Schnur 7-5 6-4 in the opening round.
Kevin Anderson – the 2018 champion in New York – was stunned 7-6 (8-6) 6-4 by qualifier Jason Jung, who will face Cameron Norrie after the seventh seed beat Brian Shi 7-5 6-3.
Elsewhere, Jordan Thompson accounted for veteran Ivo Karlovic 6-3 7-6 (7-2), Yoshihito Nishioka outlasted Henri Laaksonen 6-3 0-6 6-2, Paolo Lorenzi prevailed 4-6 6-4 6-0 over Danilo Petrovic and Go Soeda went down 6-2 6-7 (2-7) 6-3 to Kwon Soon-woo.
At the Argentina Open, Cecchinato's title defence was ended by Roberto Carballes Baena in the first round.
Cecchinato was upstaged 6-4 7-6 (7-3) by Carballes Baena, who saved five of six break points on the clay in Buenos Aires.
Next up is Casper Ruud after the eighth seed blitzed Pablo Andujar 6-2 6-3.
Fellow seed Laslo Djere and Albert Ramos-Vinolas also progressed to the last 16, along with Facundo Bagnis, Juan Ignacio Londero, Pedro Sousa, Pedro Martinez and Jozef Kovalik.
Edmund reached his third ATP Tour decider and first since 2018 with a 6-1 6-4 thrashing of Miomir Kecmanovic in their semi-final.
The British eighth seed needed just 71 minutes to brush past Kecmanovic, converting three of seven break points.
Awaiting Edmund in the final of the ATP 250 tournament is Seppi after the Italian veteran beat qualifier Jason Jung 6-3 6-2.
Seppi, 35, is a three-time title winner on the ATP Tour, although the last of those came in 2012.
At the Argentina Open, Norwegian eighth seed Casper Ruud overcame Juan Ignacio Londero 4-6 7-5 6-1 in their semi-final.
Ruud's win means he will become Norway's highest ranked male player ever, taking the record from his dad Christian, who reached 39th in the world in 1995.
Into his second ATP final, Ruud will face Pedro Sousa after the lucky loser's run continued.
Sousa moved through after Diego Schwartzman withdrew from their semi-final due to a leg injury.
The Argentinian had struggled late in his win over Pablo Cuevas on Friday, when he needed three hours, 41 minutes to advance.
Briton Edmund – contesting his first ATP Tour final since 2018 – claimed a 7-5 6-1 victory in New York.
The eighth-seeded Edmund prevailed over Italian opponent Seppi after one hour, 21 minutes for his second ATP crown.
Edmund, who reached the 2018 Australian Open semi-finals, used his serve to see off Seppi on the American hard courts at the 250 tournament.
The South Africa-born Edmund won 31 of his 33 first serve points and did not face a break point throughout the match.
Edmund broke three times en route to his first trophy since winning the 2018 European Open in Belgium.
Murray won his opening singles match at the six-day charity event – organised by his brother Jamie – against Liam Broady on Tuesday.
But despite taking the opener at the National Tennis Centre in Roehampton, the former world number one was unable to make it two victories from two.
Instead, it was Edmund, who defeated James Ward in his opening match, who secured his place in the semi-finals when Murray looped a backhand return out of play.
"Finding a way really, getting through it. It wasn't like I was down [in breaks] but I was down after the first set," Edmund told Amazon Prime following his triumph.
"Then there was a period where it was scrappy a bit, a few errors from me and you could tell he was slowly building.
"I just told myself to hang in and give myself a chance. He just puts balls in the court, he has very good anticipation, uses the area of the court very well, uses different speeds.
"Everyone wants to win and do their best. You are still playing Andy Murray, a guy who has won so much."
Despite his defeat, Murray can still make the semi-finals should he overcome Ward in his next outing.
In his first competitive action since appearing at the Davis Cup Finals in November, the three-time grand slam winner recorded a 6-2 6-2 win over Liam Broady on Tuesday.
Murray admitted beforehand that he had little chance to practice before taking part in the exhibition tournament at the National Tennis Centre in Roehampton, stating before his opener that his main aim was to "get through" it with his body holding up.
The Scot has been troubled with a pelvic injury but, with his serve working well and showing the occasional glimpse of his undoubted quality, he proved far too strong for Broady.
Still, he refused to get too carried away with his performance, describing it as "okay" during his post-match interview with Amazon Prime Video.
"I served pretty well, I thought I served well throughout the match. A lot of free points there – I've been working on my serve quite a lot," Murray said.
"I didn't hit the ball that well from the back of the court, quite a lot of errors and my balance didn't feel great. I wasn't timing the ball very well, but it was alright.
"For a first match in seven months, I've not been practising much and not even doing that well in practice matches, it was alright."
However, Murray is expecting to have problems on Wednesday when he attempts to deal with Edmund, who began his campaign by beating James Ward.
"He's fit, hitting a big ball, so I'd be surprised if I manage to come through that one," the world number 129 said of his next opponent.
"If I serve like I did today and hit the ball better a little bit cleaner from the back of the court, I'll give myself some chances. But it will be tough."
The event, organised by Jamie Murray, is following strict health guidelines as it is taking place amid the coronavirus pandemic.
Schwartzman, the top seed in Buenos Aires, needed three hours, 41 minutes to edge Pablo Cuevas 5-7 7-6 (13-11) 7-5 in an epic battle at the ATP 250 tournament.
The Argentinian, last year's runner-up, saved four match points in the second set before overcoming Cuevas.
Schwartzman managed two breaks of serve in the deciding set, including the decisive one in the 12th game.
Awaiting him in the semi-finals is Pedro Sousa, the lucky loser continuing his run with a 7-6 (7-5) 6-4 victory over Thiago Monteiro.
Casper Ruud will face Juan Ignacio Londero in the other semi-final after their respective wins over Dusan Lajovic and Guido Pella.
At the New York Open, Opelka's title defence came to an end with a 5-7 6-4 6-4 loss to qualifier Jason Jung.
Opelka served 24 aces, but the 2019 champion was broken twice to fall to defeat in one hour, 52 minutes.
Jung will meet Andreas Seppi in a semi-final after the Italian veteran got past Jordan Thompson 6-7 (2-7) 6-4 6-1.
Kyle Edmund advanced thanks to a 3-6 6-2 7-6 (7-5) win against Kwon Soon-woo, while Miomir Kecmanovic beat Ugo Humbert 3-6 6-2 6-4.
A day after first and third seeds Fabio Fognini and Karen Khachanov were knocked out, second seed Shapovalov was beaten 7-5 6-4.
Humbert, who broke serve in the final game of each set, described the win as "one of the biggest of my career" as he set up a semi-final against John Isner.
The American was taken to two tie-breaks by Kyle Edmund but prevailed 7-6 (7-5) 7-6 (7-5), his 25 aces getting him over the line as he seeks a third title in Auckland.
Benoit Paire reached his first semi-final at the event, coming from a set down to beat John Millman 3-6 6-1 6-4.
The fifth seed will face Hubert Hurkacz, who spurned six second-set match points in a mammoth tie-break before eventually seeing off Feliciano Lopez 6-4 6-7 (11-13) 6-4.
At the Adelaide International, home favourite Alex Bolt was soundly beaten by Felix Auger-Aliassime, the Canadian needing just 55 minutes to win 6-3 6-0.
He will meet Andrey Rublev in the last four after the Russian battled past Dan Evans 6-4 3-6 6-3 in just over two hours.
Spanish hopes were extinguished in the quarter-finals, where Tommy Paul surprised Albert Ramos-Vinolas to win 6-3 6-4 and Lloyd Harris beat fourth seed Pablo Carreno Busta 6-3 6-3.
Dominic Thiem cruised through the first round of the Madrid Open in straight sets on Thursday, while former winner Andy Murray suffered an early exit.
Thiem, who has twice finished as runner-up at this event, made short work of Britain's Kyle Edmund in a 6-4 6-1 win to set up a second-round meeting with fourth seed Stefanos Tsitsipas.
The Austrian won 86 per cent of points on his first serve (24 of 28) and saved all four break points against him as Edmund just could not get himself into the contest.
Elsewhere, Murray, who claimed titles in Madrid in 2008 and 2015, could not embark on another such run, with the veteran dispatched by Andrea Vavassori in a 6-2 7-6 (9-7) defeat.
The Italian was particularly dominant at the net against Murray, winning 13 of 17 such points, while the 35-year-old managed just five of 14.
Qualifier Roman Safiullin saw off a fightback from Chile Open winner Nicolas Jarry to progress 6-2 3-6 6-3, setting up a clash with Tommy Paul in the second round, while Dusan Lajovic followed up his win at the Srpska Open by beating Jason Kubler 6-3 6-3.
Thompson overcame big-serving American Isner – who had a first-round bye – 7-6 (7-2) 6-7 (3-7) 6-3 in New York on Thursday.
Isner was playing his first match since being forced to retire from his third-round clash against Stan Wawrinka at the Australian Open due to a foot injury.
Thompson lost to Isner in last year's New York quarter-finals but the Australian turned the tables after two hours, 31 minutes.
"I'm pretty stoked about that. That was a tough match," Thompson said. "I didn't get too many looks at Isner's serve, but managed to get the one break and held onto it."
Standing in the way of Thompson and the semi-finals is Andreas Seppi.
Opelka opened his title defence by cruising past Yoshihito Nishioka 6-4 6-4 at the ATP 250 tournament.
Next up is qualifier Jason Jung, who stunned seventh seed Cameron Norrie 6-4 6-4, Kyle Edmund – the eighth seed – was too good for German Dominik Koepfer 6-2 6-4.
At the Argentina Open in Buenos Aires, Diego Schwartzman and Guido Pella moved through to the quarters on clay.
Schwartzman – the top seed – prevailed 6-3 4-6 6-2 over Federico Delbonis and second seed Guido Pella survived a marathon against Facundo Bagnis 7-6 (7-2) 6-7 (2-7) 6-4.
Fellow seeds Laslo Djere and Albert Ramos-Vinolas, however, crashed out following defeats to Juan Ignacio Londero and Pablo Cuevas.
The world number one had few issues in his previous outing as he improved to 24-0 for the year, but Edmund did initially cause Djokovic problems at Flushing Meadows.
Edmund, ranked 44 in the world, claimed the first set in a tiebreak as the possibility of a shock reared its head, but Djokovic stepped up thereafter and rarely looked in trouble.
After three hours and 13 minutes on court, Djokovic eventually saw off Edmund to set up a meeting with Jan-Lennard Struff in the third round.
Edmund more than held his own in a tight and well-matched first set, the Briton proving particularly adept when coming to the net as he read a couple of Djokovic drop shots to good effect.
Neither player could break the other's serve and the first set ultimately went to the tiebreak, but Djokovic was on the back foot early on as Edmund initially edged ahead.
A wayward cross-court shot at 5-5 from the Serb gifted his opponent a golden opportunity, which he grasped with a ferocious serve straight down the middle to take the lead.
But Djokovic's response was relatively swift, securing the first service break in the fourth game of the second set when an Edmund double fault proved decisive.
Djokovic saw out the set relatively comfortably, sealing it with an ace, before then cranking his game up another level and taking charge of the third with successive breaks, the second of which was to love.
The pair traded another trio of breaks in the following three games, with both players bizarrely error-prone, but Djokovic did eventually close the set out at the fourth time of asking.
Djokovic, seemingly anticipating few issues for the remainder of the match, let out a scream of joy as Edmund failed to hold his serve again at the start of the fourth, and the 17-time grand slam champion cruised thereafter to finish off the 25-year-old's resistance.