"Ashwin is galloping towards legendary status. He is already showing himself to be a great bowler and cricketer. The way he is batting and bowling, he will be a legend when he finishes his career," Gavaskar told NDTV on Monday.
Ashwin finished with a 10-wicket haul at Kanpur's Green Park Stadium as India beat New Zealand in the first Test by a massive margin of 197 runs to take a 1-0 lead in the three-match series.
On being asked to compare Ravichandran Ashwin with other spin greats, the 67-year-old batting legend said in his exclusive chat with NDTV: "Opposition has been different when Anil Kumble and Harbhajan Singh played and when the four great spinners played. But Ashwin has got a huge heart and is a keen student of the game who is looking to get better every single day. He will certainly leave a mark on the game with both bat and ball."
The 30-year-old Chennai-born on Saturday became the fastest Indian bowler to pick up 200 wickets in Tests. He took 37 matches, nine less than Harbhajan whose record he broke.
Gavaskar praises Ravindra Jadeja, Anil Kumble
But not just Ashwin, left-arm orthodox spinner Ravindra Jadeja also performed brilliantly at Kanpur as he helped bring about New Zealand's collapse in the first innings, earning him the the Man of the Match award.
"Jadeja deserved the Man of the Match award. It is good to have three-four people in contention for the award as it means most of the players in the team have done well," Gavaskar, who played for India from 1971 to 1987, said.
The victory also marked Anil Kumble's first victory at home as the head coach of the Indian cricket team. Gavaskar feels the former leg spinner's contribution has been invaluable for the home team.
"As a coach, Kumble has been superb so far. His inputs must have been invaluable at the end of Day 1, when it was just one wicket down for New Zealand. The manner in which India struck back the next day in the first innings and got New Zealand dismissed for not too many, he must have told them what line and length to bowl and that made a big difference," said the former India skipper.
"This is where somebody who has played a lot of cricket, who has been a part of a winning team and who has been captain, can make a huge difference and we are begining to see it. It's early days as far as Kumble is concerned but the beginning has been very good and impressive."
Gavaskar, who was the first to reach 10,000 Test runs, also had a word of praise for the visiting team, saying that there is plenty to look forward to from the Black Caps.
"New Zealand didn't give up at all. They fought very well. There is plenty in this New Zealand side to like about and look forward to in the next two matches," concluded Gavaskar.
The second Test of the series will be played at the iconic Eden Gardens from September 30 to Ocotber 4. This will be India's 250th Test at home.