England, set a record-breaking target of 457 for victory, were dismissed for 186 shortly before lunch on the final day of four.
Off-spinner Rana took 4-42, removing Amy Jones for 54 and finishing the landmark match when she bowled Sophie Ecclestone for 50. Sharma chipped in with the wickets of Issy Wong and Lauren Bell as England crumbled.
India were dominant in all aspects of a game being played 142 years, and 150 matches, after Lord’s staged its first men’s Test and decades on from the London ground’s first women’s game of any kind – a 1976 one-day international between England and Australia.
Victory meant India ended their tour with happy memories of Lord’s, having been knocked out of the T20 World Cup in the group phase at the ‘Home of Cricket’ by eventual champions Australia.
England, by contrast, struggled to adapt to the demands of the longer format in a match that started just days after their T20 World Cup final loss to Australia on July 5.
The match was a personal triumph for India’s Kranti Gaud and Yastika Bhatia, the first women to take five wickets and score a century respectively in a women’s Test at Lord’s.
Gaud took a superb 5-37 in England’s first-innings 170 and wicketkeeper Bhatia’s 113 was the cornerstone of India’s imposing second-innings 341-7 declared.
England resumed on 130-6, still 327 runs shy of an unlikely win.
The highest successful fourth-innings chase in any women’s Test is Australia’s 198 against England in Sydney in 2011.
England’s hopes of at least keeping India at bay rested with Amy Jones, 52 not out overnight after completing her second fifty of the match.
The wicket-keeper, however, had added just two runs to her total when, in Monday’s third over, she lost her balance trying to pull Rana and gave a simple catch to Shafali Verma at mid-wicket.
Gaud ought to have had a wicket with her first ball Monday. Sophie Ecclestone was on eight when she edged an intended drive that burst through Rana’s hands at second slip.
Ecclestone had another reprieve on 16, with Gaud again the unlucky bowler, this time wicketkeeper Bhatia spilling the one-handed chance.
These were rare blemishes by India, however, and off-spinner Sharma took two wickers in quick succession to leave her side on the brink of victory as England slumped to 159-9.
Wong, who hung around gamely for 33 balls, was bowled for one playing down the wrong line and Lauren Bell fell for a duck when bowled by a classic off-break from Sharma that spun between bat and pad.
India thought they had won the match when Ecclestone, who had taken five wickets on Sunday, was given out lbw on 44 to Sharma attempting a sweep. But her review revealed a feint edge.
Ecclestone then added to her fine performance with the ball by completing a 61-ball fifty.
But the end came when Ecclestone was bowled by Rana’s excellent off-break to the delight of a vocal contingent of India fans basking in another sun-drenched day at Lord’s. (AFP)
