Kyle Mayers, who had taken two early wickets and featured in two other dismissals, was entrusted with the final over with India runs away from victory.
He looked on course to deny the visitors until a full-toss was smashed for a straight six by Patel to obliterate the previous record of 272 by the West Indies against Pakistan in 1988 as the highest success ODI run-chase at the venue.
"When I went out there we were aiming to get 10-11 runs-per-over," said Patel after receiving the "Man of the Match" award. "We thought it could be done because of our IPL (Indian Premier League) experience."
Shreyas Iyer (63) and Sanju Samson (54) had gotten India back on course after early setbacks, but it was Patel's intervention which made all the difference.
Hope's 13th ODI century earlier in the day, just his second in the Caribbean, came off 227 balls and was decorated with eight fours and three sixes.
He received good support from Nicholas Pooran as the home captain stroked 74 in a 117-run fourth wicket partnership with the opening batsman to justify his decision to bat first.
Mayers, West Indies top-scorer in the first match two days earlier which India won by just three runs, again set the pace with a brisk 39 in an opening stand of 65 with Hope.
Seam bowling all-rounder Shardul Thakur was the leading wicket-taker with three for 54, removing Pooran, Rovman Powell and then Hope to peg back their opponents who looked on course for a total closer to 330.
"Axar played well and we didn't hold our nerve," Pooran admitted in reflecting on a second nail-biting loss in three days. "We just could not keep things under control in the last five overs."