Eswarah held on from Something Exciting to give Michael Jarvis his first Oaks victory at Epsom.
The 11-4 joint favourite, ridden by Richard Hills, also enjoying his first Oaks win, denied a fairytale story for the runner-up's trainer David Elsworth.
Elsworth, who trained the great horses Desert Orchid and Persian Punch, was seeking his first British Classic win.
But Something Exciting (7-1) just could not reel in the unbeaten Eswarah, with Pictavia (8-1) staying on in third.
Virginia Waters, the other joint-favourite, weaved her way through the pack after the turn for home but did not get the trip, finishing fourth.
Magical Romance, who had set the earlier pace, stayed on well to come fifth.
Eswarah emulated her dam Midway Lady, who was successful in 1986, by winning the fillies' contest.
"Her dam was very good, but this filly is exceptional. She has trained beautifully," said Jarvis of the winner.
"She's done it well. I thought Richard may have gone too soon with her, but it seems to have been the right thing to do."
It was the 66-year-old trainer's second British Classic victory, coming after Ameerat won the 1,000 Guineas in 2001.
Jockey Hills told the BBC: "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."
Eswarah could now run in the Irish Oaks on 17 July although Jarvis hinted that the Yorkshire equivalent was a more likely target.
Vodafone Oaks (Group One)
Epsom, 1m 4f
1 Eswarah (R Hills) 11-4 jf
2 Something Exciting (T Quinn) 7-1
3 Pictavia (K Manning) 8-1
12 ran. Dist: ½l, 3l.