Pakistan's Shaheen Shah Afridi congratulates Indian players for their win in the Asia Cup match in Colombo, Sri Lanka, on Monday. AP
Kohli (122) and Rahul (111) put together 233 runs as India reached 356-2, a total defended after they bowled out Pakistan for 128 in the 50-over contest in Colombo.
Pakistan ended on 128-8 in 32 overs with injured bowlers Haris Rauf and Naseem Shah not turning out to bat. India spinner Kuldeep Yadav returned figures of 5-25 to hand India their biggest ODI win over Pakistan.
India resumed on 147-2 after rain ended play early on Sunday and pushed the match into an additional day set aside by the tournament, which is a precursor to the ODI World Cup.
Rain again delayed the start but no overs were lost and then the Kohli-Rahul pair roused the Indian fans at a largely empty stadium.
"KL and myself are both conventional players. And when you have him batting the way he was and me playing, its tough to break these partnerships because we don't play fancy shots," man of the match Kohli said on the marathon stand.
Kohli added, "It is one of the memorable partnerships we've had and for Indian cricket as well. He (Rahul) hit form for us straightaway, good for us."
Rahul, who returned from an injury lay-off, raised his bat to celebrate his hundred and was hugged by Kohli, who soon brought up his own ton after surpassing 13,000 ODI runs.
It was Kohli's 47th ODI ton and extended his century score to 77 in internationals.
Half-centuries from skipper Rohit Sharma and fellow opener Shubman Gill got India off to a good start on Sunday with a 121-run stand.
Kohli and Rahul resumed cautiously on their overnight scores of eight and 17 before they took to the Pakistan attack with 100 runs in 102 balls.
Pakistan suffered a blow when officials said fast bowler Rauf had suffered a strain and would take no further part. Later fellow quick Naseem also walked off with some discomfort to his hand.
Rahul smashed 12 fours and two sixes, including whipping Shadab Khan over mid-wicket, in his 106-ball knock.
Kohli finished the innings with a six down the ground against a bowling attack that lacked sting. Sloppy fielding added to Pakistan's woes.
Pace spearhead Shaheen Shah Afridi and Shadab got a wicket each on Sunday.
Ground staff worked tirelessly to get the field ready after Monday's early rain and received "big thanks" from Rohit and Kohli.
Pakistan were never in the chase after they lost two early wickets including skipper Babar Azam bowled for 10 off an impressive in-swinger by Hardik Pandya.
Rain once again interrupted play but not the Indian momentum as the bowlers kept up their charge after resumption and Kuldeep sent back Mohammad Rizwan with his left-arm wrist spin.
Wickets kept tumbling and Kuldeep got three more to get into the Pakistan tail and then claimed his second ODI five-wicket haul.
Azam said, "we lost back-to-back wickets, couldn't build partnerships".
The extra day was a last-minute addition to the Super Four clash - the only game to get the advantage other than the final - after a previous group game between the two teams was washed out in Pallekele.
India will head into a third successive day of cricket when they meet Sri Lanka in the next Super Four clash on Tuesday at the same venue.
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