It appeared the tourists stood a chance at Ranchi when Mathews, who had struck over 3,000 format runs in 137 appearances period to the game, hit a century for the first time.
Mathews' superb innings, compiled in just 116 deliveries, helped Sri Lanka to 286-8.
But while three figures had eluded Mathews in this format, Kohli collects hundreds with astonishing regularity.
And his enviable class was on full show as he racked up a 21st, 14 of which have come in run-chases.
That effort secured a three-wicket success as the world champions whitewashed their opponents in a rubber spanning more than three games for the first time since 1982.
Sri Lanka endured a difficult start after losing the toss, Niroshan Dickwella hitting a Dhawal Kulkarni slower ball to square-leg.
Things got worse in the next over when Stuart Binny bowled Tillakaratne Dilshan - who had struck a 24-ball 35 - through the gate as the opener attempted an ambitious cover-drive.
That preceded a grim innings from Dinesh Chandimal, who used up 31 in compiling just five before skying an attempted to slog-sweep off Akshar Patel to mid-on.
Yet that merely heralded the arrival of Mathews, who finally broke his duck with an innings for the ages.
Having utilised 75 balls to compile 45, the skipper exploded into life later in his knock.
Particular strong through the leg side, he hit an astonishing 10 sixes - three of which came in the same Patel over.
Lahiru Thirimanne offered decent support with 52, while Kulkarni claimed 3-57 in his eight overs.
Mathews' effort would prove in vain, however, as Kohli equalled his innings, albeit without the same rope-clearing pyrotechnics.
Having entered the fray after Mathews backed up his batting heroics by castling Ajinkya Rahane and Rohit Sharma - who hit an incredible 264 in the last encounter - Kohli immediately assumed control.
Mixing good running with beautifully timed boundaries to great effect, the number four put Sri Lanka to the sword in spectacular fashion.
Initially aided by Ambati Rayudu's 59, he single-handedly took India over the line amid Ajantha Mendis producing a fine late burst.
With the hosts seemingly cruising, the spinner ousted Robin Uthappa, Kedar Jadhav, Binny and Ravichandran Ashwin in quick succession to leave the game in the balance.
Kohli did not blink, though, and finished the job when striking Mendis for two maximums in three balls to end his 126-ball masterclass.