Mogul was ridden by his trainer's son Donnacha O'Brien when he made his racecourse debut on 14 August in a maiden race over one mile at Gowran Park in which he started the 5/4 favourite and finished second to the Jim Bolger-trained Geometrical. The colt was partnered by Ryan Moore when he recorded his first success in a similar event at the Curragh, leading from the start and coming home three and a quarter lengths clear of his eleven opponents at odds of 8/13.[5] Moore was again in the saddle when Mogul was stepped up in class and started 1/2 favourite for the Group 2 Champions Juvenile Stakes over one mile at Leopardstown Racecourse on 14 September. He raced in fourth place as his stablemate Cormorant set the pace before moving up to take the lead a furlong and a half from the finish and kept on well to win by one and a quarter lengths from the second favourite Sinawann.[6] After the race Aidan O'Brien commented "We were delighted with him. He was trapped a little bit wide today and there was a nice pace on so he learned plenty... we've been very happy with his progress form race to race so hopefully he'll progress on again... We won't over-race him... we think he's a Classic horse".[7]
The Group 1 Vertem Futurity Trophy had been planned for Doncaster Racecourse on 26 October but owing to the waterlogged state or the turf track it was rescheduled to take place six days later on the synthetic Tapeta surface at Newcastle Racecourse. With Donnacha O'Brien in the saddle, Mogul started second favourite but despite racing making good progress from the rear of the field in the last quarter mile he came home fourth behind Kameko, Innisfree and Year of the Tiger.[8]
The 2020 flat racing season in England and Ireland was disrupted by the COVID-19 pandemic and Mogul did not make his reappearance until 16 June when he was sent to England to contest the Group 2 King Edward VII Stakes over twelve furlongs at the Royal Ascot. Owing to the restructuring of the programme the race became, for the first time, a trial race for the Epsom Derby. He started the 10/11 favourite but after racing towards the rear of the six-runner field he was unable to make any real progress in the straight and came home fourth behind Pyledriver. The 241st running of the Epsom Derby took place a month later than usual, behind closed doors, over one and a half miles at Epsom Racecourse on 4 July and Mogul started the 7/1 third favourite in a seventeen-runner field. Ridden by Moore he raced in mid-division before making steady progress in the straight but never looked likely to win and finished sixth behind his unfancied stablemate Serpentine beaten seven lengths by the winner.[9]
On 30 July at Goodwood Racecourse Mogul contested the Group 3 Gordon Stakes and went off the 9/2 third choice in the betting behind English King (winner of the Lingfield Derby Trial) and Al Aasy (Bahrain Trophy) in a field which also included Subjectivist (Glasgow Stakes) and Khalifa Sat (runner-up in the Derby). Moore positioned the colt just behind the leaders before moving up on the outside in the straight. He gained the advantage inside the final furlong and won by three quarters of a length from Highland Chief.[10] After the race Aidan O'Brien said "We always felt he was a lovely horse, but we always felt he was going to take two runs and we were hoping to get that into him before the Derby. Obviously the Derby was only his second run and today was his third... he's a big, strong, powerful horse who carries a lot of weight, so it was always going to take racing to get him tuned up. We were delighted with him today and we still think there's more to come from him".[11]
Mogul reappeared in the Great Voltigeur Stakes at York Racecourse on 19 August and started favourite but after being contention for most of the way he was beaten into third place behind Pyledriver and Highland Chief. On 13 September Mogul was sent to France for the Grand Prix de Paris over 2400 metres at Longchamp Racecourse in which he was ridden by Pierre-Charles Boudot. The race had previously been run in June or July but had been rescheduled owing to the COVID-19 Pandemic. He was made the 8.5/1 fifth choice in the betting behind Port Guillaume (Prix Hocquart), Serpentine, English King and In Swoop (Deutsches Derby). Mogul raced towards the rear of the field as his stablemate Nobel Prize set the pace but made rapid progress along the inside rail in the straight before being switched left and taking the lead 300 metres from the finish. He quickly established a clear advantage and won by two and a half lengths from the fast-finishing In Swoop.[12] O'Brien who watched the race on television said "He's been showing so much speed, I thought we might be going the wrong way and maybe we should be going back to a mile and a quarter... He's obviously a fast horse, and he's able to quicken".[13]
The colt was scheduled to run in the Prix de l'Arc de Triomphe on 4 October but the O'Brien contingent was withdrawn en masse when four horses failed drug tests, with the results being attributed to a batch of contaminated feed.[14] Mogul was then sent to the United States and matched against older horses for the first time as he contested the Breeders' Cup Turf at Keeneland on 7 November. Starting the third choice in the betting he produced a sustained run from the rear of the field but never looked likely to win and came home fifth behind Tarnawa, Magical, Channel Maker and Lord North, beaten three lengths by the winner. On 13 December Mogul was sent to Sha Tin Racecourse in Hong Kong to contest the Hong Kong Vase over 2400 metres in which he was ridden by Moore and started the 1.6/1 second favourite behind the locally-trained Exultant, who had won the race in 2018. After settling in fourth place he moved up alongside the front-running Exultant in the straight before pulling clear in the closing stages to win by three lengths.[15] After the race Moore said "He's a horse that we always expected a lot from... the race worked out nicely for him... He’s put them away very nicely. In reality, I was in front sooner than would have been ideal today but he took me there nicely. When he gets in front, he maybe lacks a bit of concentration still but he’s a beautiful looking horse. He's got a fantastic mind and it doesn't stress him. He'll be a really nice four year-old."[16]
In the 2020 World's Best Racehorse Rankings, Mogul was rated on 121, making him the equal 34th best racehorse in the world.[17]