The 32-year-old Harbhajan, who has taken more than 400 test wickets, struggled during India's dismal tour of England last year in which he claimed two wickets in the first two tests before an abdominal strain cut short his trip.
The team was whitewashed 4-0 in the test series and went on to lose their number one ranking without winning a single match on the tour.
With Harbhajan unavailable, India selectors turned to Ashwin and the 25-year-old spinner has not let them down.
Hailing from the southern state of Tamil Nadu, Ashwin has made full use of his chance to shine on the big stage and racked up 34 wickets in four tests on home soil.
He picked up the man-of-the-series award in his debut series against West Indies and took a career-best 12 wickets against New Zealand in Hyderabad to help guide India victory by an innings and 115 runs in the opening test on Sunday.
With England and Australia each scheduled to play a four-match series in India later this season, the hosts have an ideal opportunity to make up for their eight consecutive away test defeats to the same opponents last year.
In Ashwin, India have found a potent weapon to torment the visitors on the slow pitches at home as New Zealand captain Ross Taylor was quick to point out.
"We need to learn how to play Ashwin and... play him a lot better," Taylor said after the heavy defeat in the opener of the two-match series.
Ashwin has forged a strong partnership with left-arm spinner Pragyan Ojha, the duo sharing 60 wickets in the four tests they have played together.
They may still be a long way from becoming a strikeforce similar to the one formed by leg-spinner Anil Kumble and Harbhajan, but all the early signs are encouraging.
"Ojha is someone who I have played with since I was 16 and we have always enjoyed each other's company," Ashwin told reporters on Sunday.
"I was a batsman then when Ojha was a prime bowler but I still used to bowl in one-day games. We always used to bowl well together because we used to build pressure very well."
Ashwin may lack the variation of Harbhajan but he does possess excellent control over his line and length, and bowls very few loose deliveries.
India captain Mahendra Singh Dhoni praised his spin twins for their ability to maintain pressure on opposing batsmen.
"I think the bowlers bowled brilliantly. They didn't give any loose deliveries to score runs which meant even if the opposition batted for one or two hours, the score was not picking a lot," Dhoni said.
"That really made the difference as we could have those catching fielders and put pressure on them."
Ashwin has the advantage of height, which he uses well to extract bounce off the wicket, and his 'carrom ball' is also very effective on turning wickets.
He is also a useful batsman lower down the order, already boasting a test hundred and a batting average of more than 35, which makes Harbhajan's comeback even more unlikely.