Sweating up badly before the race, the Michael Jarvis-trained filly drifted in the betting ring to share favouritism with Virginia Waters at 11-4.
But in the words of jockey Richard Hills, the race “went like clockwork” for Eswarah, who was scoring 19 years after Midway Lady.
Deviating slightly from the planned tactics, Hills’ mount swept through to go clear two furlongs out.
And although David Elsworth’s Something Exciting threw down a challenge in the final furlong, Eswarah denied the trainer a first Classic success by half a length.
Three lengths further adrift, Irish hope Pictavia stayed on late to grab third place ahead of compatriots Virginia Waters and Silk And Scarlet.
Hills had Eswarah settled in the pack in the early stages while Magical Romance set a strong early pace along with Mona Lisa.
Dream To Dress briefly took it up entering the straight, but Hills then pushed the button and Eswarah hit the front with a burst of accleration that none of her rivals could match.
It was the same burst of speed which, according to Jarvis and Hills, the filly has been showing regularly on the home gallops in Newmarket.
“She did improve a lot after her first race and it is always nice when you watch a nice horse do their work and put three lengths between them and a decent lead horse,” Jarvis said.
“The thing was she was doing it so well that as the race got nearer I started to get worried that I had done too much with her, and we had to put the brakes on a little bit.
“Epsom has been a very lucky track for me. I was lucky enough to lead up a Derby winner when I was a stable lad and now I have trained a winner of the Coronation Cup and the Oaks.
“It might not be everybody’s cup of tea but I love the place!”
Jarvis, 66, sending out his second British Classic winner, was also quick to give some of the credit to Ben Hanbury, who handled Eswarah as a juvenile before retiring at the end of last season.
He said: “Her dam was very good, but this filly is exceptional. She has trained beautifully.
“All credit to Ben, in his retirement he’s been very helpful and all the way along he has said ‘This filly is good’. But I said to him ’Just good? She’s better than that’.
“We had a plan to hold her up a little longer but I think Richard saw Kieren going well on the inside and decided to kick on.
“I was willing the winning post to come, especially when the runner-up came at us, but she did everything bravely.”
Hills, who screamed with joy as he breasted the winning line ahead of his rivals, enjoyed a perfect passage but paid tribute to his mount, who lacked the experience of many of her rivals.
“I was conscious that with a filly who had only two runs, I didn’t want to be on the inside, so I gave her a chance to see some daylight and to give her every chance of handling the course,” he said.
“I didn’t want her bumped all the way round. I thought it might frighten her.
“Everything went well from there. I followed them into the straight and it was then a matter of waiting before I pounced.
“They slowed up about six furlongs out, which was good because my filly got a good breather into her for the run-in.
“I just wanted her to produce the turn of foot that she has always showed at home.
“Each time I have been to ride her at Michael’s I have just got off and we’ve smiled at each other, because there was no need to say anything.
“She got a bit warm at the start because she wanted to get on with it, but these fillies do that.”
Having bred as well as owned the winner, Hamdan Al Maktoum described the result as a “double happiness”.
“The trainer said that she gave him the feel of a very good filly,” he said.
“I saw her twice last season with Ben and he said that she wasn’t right, she was lame. She was certainly never among our best two-year-olds.
“But Ben gave her time and now here she is winning such a good race.”
Plans for the winner may involve sending her to the Curragh for the Irish equivalent on July 17.
But Jarvis hinted that the Yorkshire Oaks might be a likelier target, given the busy period she has undergone of late.
“Sheikh Hamdan said to me that as she has run three times in five weeks it might be a bit much, even though Ireland is the obvious way to go,” the trainer commented.
“She’s had a couple of smacks on her backside for the first time in her life today so we’ll have to see how she comes out of this first.”