Murray had won his previous seven meetings with the Belgian, but entered this clash in poor form and revealed last week it was likely he would end his decorated tennis career this summer.
The three-time grand-slam champion appeared rejuvenated following his announcement in Dubai and put in one of his best displays of the year to claim a routine 6-3 6-2 victory, which sets up a last-64 clash with Andrey Rublev.
In a nip-and-tuck first set, Murray had to be patient after a break point in Goffin’s opening service game was held before he was able to strike when 4-3 up.
Murray claimed his first break of the match in the eighth game and sent down two aces to seal a 34-minute opener where he won the final 10 points.
The momentum was with the British number four now and a double-fault by Goffin handed him an early advantage in the second set.
World number 61 Murray continued to ask questions of Goffin’s serve and a second break arrived to put him on the verge of a place in the last-64, which was sealed with an ace.
Compatriot Jack Draper suffered disappointment as he lost in three sets to Chris O’Connell in the first round of the BNP Paribas Open.
British prospect Draper had defeated Murray on his way to the last 16 of the tournament in 2023 but lost six games in a row in the final set to go down 1-6 6-3 6-2 to his Australian opponent.
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It continued a frustrating period for Draper, who made the semi-finals of the Mexican Open last week but had to retire during his last-four clash with eventual champion Alex de Minaur.
Draper initially showed no ill-effects after he had battled food poisoning in Acapulco and eventually edged a lengthy fourth game to go 3-1 up before he saved a number of break points to consolidate his advantage.
Another break followed to allow the world number 37 to take the opener 6-1 but he sent down two double faults at the start of the second to hand O’Connell the initiative.
The Aussie did not look back and forced a decider, which started with Draper saving four break points before he broke to go 2-0 up.
Draper ran out of gas though, with world number 66 O’Connell booking a second-round meeting with Alexander Zverev.
The world number two took only one hour and 42 minutes to claim victory, marking Alcaraz’s first title since his triumph at Wimbledon last year.
The 20-year-old Spaniard began the Indian Wells tournament with a 6-3 record on the season and an injured ankle, which he sustained during his latest outing in Rio de Janeiro.
Medvedev started strong in the match’s opening rounds, establishing a 3-0 lead as Alcaraz’s errors began to pile up.
It did not take long for Alcaraz to find his feet though, breaking back before matching the world number four to force a tie-break.
He almost let an early lead in the tie-break slip by, but recovered again to take the first set in just over an hour.
Once he had broken out in front, the world number two was barely troubled in the second set en route to retaining his Indian Wells title.
He told reporters on-court after the match that the win had bolstered his confidence following his Rio injury scare.
“Winning this tournament means a lot to me because the week before it began, I had a lot of doubts about my ankle,” Alcaraz said.
“I remember my first practice here was just 30 minutes with no movement, and probably the first practice with really good tennis players was really tough for me because I thought I was not going to play my best.”
He added: “I was not feeling well with my ankle, so a lot of doubts for me. But once I stepped on the court, the first round, I started to feel better.”
Australian Open champion Sinner had won 16 straight matches to begin the year – and 19 in all stretching back to last season – but the number three seed had no answer to the Spaniard after winning the first set.
Defending Indian Wells champion Alcaraz was broken twice after a three-hour rain delay as Sinner raced to a 6-1 first set victory.
But having faced deuce on his opening service game of the second set, the Spaniard grabbed the initiative with an early break.
He saved break points in successive games and served out to level the match.
Alcaraz, who would have surrendered the world number two spot to Sinner with a defeat, again broke early in the deciding set.
He dropped just three points on his serve, rattling off five straight games to lead 5-1, clinching victory on his third match point in just over two hours.
“I stayed strong mentally,” said Alcaraz. “I think that’s a really important part in this game. You have to be strong mentally if you want to overcome these kind of matches, a set down against someone that’s playing an unbelievable game.
“I changed my style a little bit, I changed my game a little bit and I think it worked very well. I’m really happy to beat Jannik and be in the final again.”
The Spaniard, bidding to become the first player to defend the title since Novak Djokovic in 2016, won 6-3 6-3 in an hour and a quarter.
Hungarian Marozsan, 24, came into the match with a rare winning head-to-head record against Alcaraz, having beaten him on the Rome clay last year in their only previous meeting, one of the shock results of the season.
The Wimbledon champion quickly went about taking his revenge, winning four games in a row from 3-2 down to take the first set.
A solitary break for 4-2 in the second proved enough to wrap up the match and book a last-eight meeting with Alexander Zverev.
“Honestly I was nervous before the match, playing against someone who beat you, let’s say easily, it was difficult for me to approach the game,” Alcaraz said in his on-court interview.
“But I’m happy with the win. Today I knew better what I needed to do than in Rome.”
Zverev took down Australian Alex de Minaur after he lost the first set before coming back to win 5-7 6-2 6-3.
Australian Open champion Jannik Sinner continued his stellar start to the year, recording his 18th straight win in a victory over American Ben Shelton 7-6 (4) 6-1.
Stefanos Tsitsipas, the 11th seed from Greece, was on the end of an upset as he slipped to a 6-2 6-4 defeat to Czech youngster Jiri Lehecka.
It took little more than an hour for Poland’s Swiatek to beat Kazakhstan’s Yulia Putintseva in straight sets 6-1 6-2.
Wozniacki, from Denmark, defeated three-time Grand Slam winner Angelique Kerber in 90 minutes 6-4 6-2, advancing to her first WTA 1000 quarter-final since 2019 after returning to the tour.
After her match, former world number one Wozniacki said she will have to play her “best tennis to compete” with Swiatek.
“I think I have obviously commentated some of her matches,” she said. “I know how she’s playing. Obviously she’s playing good tennis, playing powerfully.
“I practiced with her as well a few times after I have come back, during the US Open as well. I know how she plays, but it’s one thing knowing how she plays and also playing against her in a full match.”
Swiatek said on court that she has great respect for Wozniacki.
“I think she’s playing great even after the maternity break. She was fighting to come back.
“I have huge respect. I’m going to prepare like any other, but off the court she’s a great person.”
Ukrainian Marta Kostyuk defeated Russian Anastasia Pavlyuchenkova 6-4 6-1, while Russian Anastasia Potapova defeated Italian Jasmine Paolini 7-5 0-6 6-3.
Boulter arrived at the tournament riding a crest of a wave after she secured a maiden WTA 500 title at the San Diego Open to continue her excellent 2024.
It earned the British number one a new career-best ranking of 27, but her momentum was checked after a 6-3 6-2 loss in quick fashion to Italian opponent Giorgi.
Giorgi entered this match in poor form and early breaks were exchanged between the duo before the first set went the way of the 32-year-old in 40 minutes.
After Giorgi claimed a decisive second break to edge the opener 6-3, two early breaks handed her the initiative at the start of the next set.
Boulter did finally get off the mark to make it 4-1 but there was no way back and she exited after a 78-minute loss.
