Despite his win in the Guineas, Paradox was passed over by Archer, who chose to ride Melton in the Derby.
At Epsom on 3 June Paradox, ridden by Fred Webb, was made the 4/1 second favourite in a field of twelve runners, with Melton starting the 15/8 favourite.
Webb was given the ride despite "scurrilous" rumours concerning his honesty.
The race took place in fine weather before a reportedly "enormous" crowd that included the Prince and Princess of Wales.
Paradox took the lead two furlongs from the finish and was immediately challenged by Archer on Melton; from that point on the two had the race between them.
Melton made gradual but relentless progress to catch Paradox "in the last stride" and win by a head in a "desperate finish", with Archer riding one of his strongest races.
After the race Cloete expressed his satisfaction with Webb's performance and rewarded the jockey with a gift of £100.
Irish writer Oscar Wilde was reported to have observed "I understand that Milton's Paradise Lost is being revived and will appear in Derby Week and will be published under the title Paradox Lost by Melton."

Paradox was never beaten again.
Eleven days after his defeat at Epsom he was sent to Longchamp to contest the Grand Prix de Paris, the most important and valuable race in France.
The start of the race was delayed for half an hour as the authorities struggled to clear spectators from the course.
Ridden once again by Archer, Paradox was restrained in the early stages before making steady progress and turning into the straight in second place.
Paradox overtook the leader Reluisant halfway down the straight and won "[w]ith the greatest ease" at odds of 1/3.
His success was greeted enthusiastically by the travelling British supporters but there were hisses and hoots from the French contingent and the raising of the Union Jack after the race led to what was described as an "unfavourable demonstration".
Paradox returned to England and ran the one mile Sussex Stakes at Goodwood on 29 July.
The winners of major races were assigned additional weight in the race and Paradox carried twelve pounds extra as a result of his success in France.
Archer sent him to the front two furlongs from the finish and he won comfortably by three quarters of a length from Royal Hampton.
Despite his win in the Guineas, Paradox was passed over by Archer, who chose to ride Melton in the Derby. At Epsom on 3 June Paradox, ridden by Fred Webb, was made the 4/1 second favourite in a field of twelve runners, with Melton starting the 15/8 favourite. Webb was given the ride despite "scurrilous" rumours concerning his honesty. The race took place in fine weather before a reportedly "enormous" crowd that included the Prince and Princess of Wales. Paradox took the lead two furlongs from the finish and was immediately challenged by Archer on Melton; from that point on the two had the race between them. Melton made gradual but relentless progress to catch Paradox "in the last stride" and win by a head in a "desperate finish", with Archer riding one of his strongest races. After the race Cloete expressed his satisfaction with Webb's performance and rewarded the jockey with a gift of £100. Irish writer Oscar Wilde was reported to have observed "I understand that Milton's Paradise Lost is being revived and will appear in Derby Week and will be published under the title Paradox Lost by Melton."
Paradox was never beaten again. Eleven days after his defeat at Epsom he was sent to Longchamp to contest the Grand Prix de Paris, the most important and valuable race in France. The start of the race was delayed for half an hour as the authorities struggled to clear spectators from the course. Ridden once again by Archer, Paradox was restrained in the early stages before making steady progress and turning into the straight in second place. Paradox overtook the leader Reluisant halfway down the straight and won "[w]ith the greatest ease" at odds of 1/3. His success was greeted enthusiastically by the travelling British supporters but there were hisses and hoots from the French contingent and the raising of the Union Jack after the race led to what was described as an "unfavourable demonstration". Paradox returned to England and ran the one mile Sussex Stakes at Goodwood on 29 July. The winners of major races were assigned additional weight in the race and Paradox carried twelve pounds extra as a result of his success in France. Archer sent him to the front two furlongs from the finish and he won comfortably by three quarters of a length from Royal Hampton.
Paradox (horse)