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While Root played an eye-catching knock of 56 in 41 balls as England quickly built up a 444-run lead before declaring, he says he was able to play the shots he did because of Cook at the other end.
England's captain followed up 95 in the first innings with an unbeaten 70 in 114 balls as England declared on 205 for four.
By stumps they had reduced India to 112 for four to give themselves a strong chance of a victory that would level the series at 1-1.
"I think as games of cricket go or days of cricket go, that's one you want to have," Root said.
"To get the two early wickets like we did was fantastic and then a lot of credit has to go to (Alastair) Cook for the way he set the game up with the bat and the pace and the way he judged his innings pretty much down to a tee.
"We wanted to have a good session at them tonight and give ourselves a decent score on the board.
"The way he played meant that guys like myself, Ian (Bell) and Gary (Ballance) could be a bit more free at the other end.
"Then to go on and take four wickets as a side was fantastic. We wanted to get at least a couple but to make good inroads into their top order was really pleasing."
While Root has been in good form throughout the series for England, Cook, Bell and fast bowler James Anderson have not been at their best.
Root says he is pleased that those three players have performed in this match.
"It's good to see a lot of guys back into form. Like Jimmy (Anderson) has got five (wickets) now under his belt. Ian (Bell) with a big 100 and (Alistair) Cook with back-to-back 50s.
"Now, pretty much everyone has contributed over the summer. Hopefully that can continue throughout the rest of this series and throughout the rest of this game."
Video courtesy of SNTV.
© Cricket World 2014