The home side had bagged the series with back-to-back wins in Mohali and Indore, rendering the result of the match at M Chinnaswamy Stadium academic.
But the final match of the three-match series provided the most drama as Afghanistan, replying to India's mammoth 212-4, racked up 212-6 resulting in a deadlock.
In the first Super Over, Afghanistan managed 16-1, which India matched as the stalemate continued.
India scored 11-2 in the second Super Over before spinner Ravi Bishnoi sealed their victory in three deliveries, conceding just one run and taking two wickets.
"My heart rate was high, but we had a lot of fun," leg-spinner Bishnoi said.
"The moment we saw two right-handers come out, I was given the ball.
"The idea was to bowl back of length to begin with from a little behind the crease."
Earlier, India looked in trouble after they slumped to 22-4 inside five overs after electing to bat.
Skipper Rohit Sharma smashed an unbeaten 121 off 69 balls as he and Rinku Singh, who hammered 69 not out, rescued India with an unbroken fifth-wicket stand of 190 off just 95 balls.
Karim Janat bled 36 runs in the final over of the Indian innings conceding six sixes in that seven-ball over that included a no-ball.
Rohit's fifth hundred in T20 Internationals was studded with eight sixes, while Rinku clobbered six sixes in his 39-ball blitz.
Rahmanullah Gurbaz (50), Ibrahim Zadran (50) and Mohammad Nabi (34) kept Afghanistan in the hunt but it was Gulbadin Naib's unbeaten 55, which helped them match India's total even though they eventually finished the series without a win.
