Shami, who delivered a man of the match-winning haul of 3/19 in the first ODI against New Zealand here, failed the 'Yo-Yo' fitness test last year and was also bogged down by some personal issues.
But putting all those troubles behind him, Shami reached the 100-wicket mark in his 56th game. On Wednesday, he dismissed openers Martin Guptill and Colin Munro in the six overs he bowled.
"The fast bowling group together believes they can knock any side over. And the belief in his (Shami) own ability and his fitness - this is the fittest I've seen him in his career. And his Test form has translated into one-day cricket," Kohli said at the post-match presentation.
Besides his injury woes, the 27-year-old Shami was troubled by allegations of domestic violence by his wife last year. He failed the 'Yo-Yo' fitness test ahead of the one-off Test against Afghanistan in June last year.
A 'Yo-Yo' test requires a player to sprint between two cones that are set 20 metres apart to the sound of a beep and is considered a reliable measure of an athlete's endurance and stamina.
Shami's comeback started in Australia, where he picked up 16 wickets in the Test series.
Speaking about India's eight-wicket win here Wednesday, Kohli said he was pleased with the all-round effort.
"It was one of our more balanced performances in the last few games. When I lost the toss, I thought it was going to be 300 par. 150-odd on that wicket was superb," Kohli said.
For India, wrist spinner Kuldeep Yadav was the most successful bowler, returning figures of 4/39 in 10 overs, while Yuzvendra Chahal and Kedar Jadhav shared three wickets among themselves.
"The pitch got slow in the second half of the innings but in the first half, the spinners bowled well, cramped the batsmen and they still made it difficult despite the dimensions of the field," Kohli said.
The skipper also praised opener Shikhar Dhawan, who was unbeaten on 75 in the 156-run chase.
"Really important innings for Shikhar and we spoke during the sun break that he needed to finish the game to get some momentum. He is a dangerous player when in rhythm," Kohli said.
Kohli's Kiwi counterpart Kane Williamson said his team was just not upto it here.
"It wasn't our best effort. We expected India to be good and they were very good. We just had to get through the slower balls but I do think their lengths were immaculate," he said.
"Obviously 150 on the board on a surface where 250 was par was hard. It was lack of adjusting to the surface. All the Indian bowlers contributed but we do need to be better," he added.
But he did touch on the positives as well.
"I do think our energy in the field and with the ball was good though and we need to move on from this game quickly," he said.