After visiting captain Vikram Solanki inserted the hosts, the local favourites put up a decent 260 for six in their allotted 50 overs.
Chasing the target of 261, the visitors lost their Udaipur-born captain in the third over of the match while dependable Owaish Shah (2) also departed early, as the pace duo of VRV Singh and RP Singh drew blood that left the English side reeling at 18 for two.
Kevin Pietersen(28) and stumper Matthew Prior (55 off 67 balls, 4X10) then stemmed the rot and put up 69 runs for the third wicket and just when KP -- as Pietersen is known as -- looked good for a big innings, he went for a non-existent run and Raina was quick to send him back.
Ian Bell (71 off 84 balls, 4x3, 6x2) and Paul Collingwood (34) kept England in the game but the visitors could not survive after four of their batsmen got run out at crucial moments.
Towards the end, it was Kabir Ali injected excitement in the match. Needing 24 in 11 balls, he hoicked Piyush Chawala over long-on for six.
Needing 12 runs from the last three balls with one wicket in hand, Kabir hit another six off Y Venugopal Rao's fourth delivery in the 50th over which saw England needing six runs in the last two balls.
But in the very next ball which Kabir drove to cover, James Anderson set off from the non-striker's end and an agile Kaif caught him short of ground to help the side clinch the thriller.
Earlier, Kaif scored an unbeaten 119 and with statemate Suresh Raina (49), forged together a 78-run partnership which laid the foundation for a win.
Gautam Gambhir (5) and Jaydev Shah (10) -- son of BCCI Secretary Niranjan Shah -- could not give RCA XI a good start and the former's bad patch got prolonged as he nicked James Anderson down the leg for stumper Matthew Prior to take the catch, while Shah fell to Sajid Mahmood as the hosts slumped to 28 for two. That brought in Kaif and Raina and the duo first steadied the ship before Raina opened up.
Raina was positive throughout and he steered Sajid Mahmood for four off the second ball he faced and he later punished James Anderson, hitting three fours in the pacer's fifth over.
One run short of a well-deserved half century, Raina perished at deep square leg where Owaish Shah caught him off Paul Collingwood.
Kaif had, by then, started playing his shots and he hit Liam Plunkett for consecutive fours and England were left without the service of Sajid Mahmood who developed a stomach cramp.
Y Venugopala Rao (14), like Gambhir, lost a golden opportunity to impress the selectors and was castled by Collingwood through the gates.
Ajay Jadeja (18) was playing against a foreign team after ages but he too could not make much of it as the RCA President's XI skipper top-edged Ian Blackwell and the hosts were reduced to 166 for five.
Kaif was unflappable on the other end and he played according to the situation and Team India discard Parthiv Patel(25) gave him good company till he was caught by Ian Bell at midwicket off Kabir Ali.
Kaif remained not out on 119 that came off 136 balls and included 11 hits to the fence besides a couple of sixes.
For English side, Collingwood was the most successful bowler, claiming two for 28 in his seven overs.