The Super Bowl MVP claimed eight catches and two touchdowns to haul the Rams back into the lead, after they fell behind just 12 seconds into the second half.
The game-winning drive in the dying minutes proved to be the difference, with Rams quarterback Matthew Stafford and Kupp leading a late charge for the host side.
Down 20-16, the duo connected on a number of big plays down the stretch, culminating in a one-yard touchdown reception to put the Rams in front with 1:25 left on the clock.
The Bengals still had an opportunity to steal the victory, but Aaron Donald and the Rams defence stepped up when it mattered most to deny Cincinnati a maiden Super Bowl win.
The Rams surged ahead early in the first quarter with Odell Beckham Jr claiming a 17-yard touchdown; leaping above Mike Hilton to gobble up a Matthew Stafford throw.
In the second quarter, Kupp extended the Rams lead to 13-3 collecting an 11-yard touchdown, though they fluffed the resulting extra point.
But Cincinnati battled back to make it 13-10 with a perfect trick play. Burrow passed it back to Joe Mixon, who threw a touchdown pass to a wide-open Tee Higgins in the endzone.
Momentum then swung in the Bengals' favour as Rams receiver Odell Beckham Jr limped off the field with a knee injury, and Bengals safety Jessie Bates intercepted a Matthew Stafford throw intended for Van Jefferson in the end zone.
Just 12 seconds into the second half, the Bengals took a 17-13 lead. Higgins claimed a 75-yard touchdown after grabbing a huge Joe Burrow throw. Higgins shrugged off the attention of Rams' Jalen Ramsey, but no flags were thrown despite contact with his face mask.
The third quarter ended 16-20 in favour of the Bengals, with both QBs under pressure and the defences on top.
After an attritional fourth quarter, with less than two minutes to go Kupp snaffled a touchdown on the edge of the end zone, after a penalty strewn final drive.
The Bengals failed to get back into the match in the last 1 minute 25 that remained, with Aaron Donald sacking Joe Burrow on the 4th and final down of the game.