Chasing an improbable 549, India were all out for 140 in the second session on the final day, with only Ravindra Jadeja (54) offering some resistance with the bat.
Aiden Markram took a record nine catches in the match for reigning world Test champions South Africa, who won the opening match in Kolkata inside three days.
"It's a great feeling, a great effort by everyone to be fair," Markram said afterwards.
"As a group, you've got to believe that you can compete against the best in their backyard and get into the battle and see where it gets you ... bloody proud of the team."
Having lost both the openers on Tuesday, India entered the final day needing to bat out three sessions to eke out a pride-salvaging draw.
The early struggles of both their overnight batters inspired little confidence though.
Sai Sudharsan (14) got a life when he was caught behind but it turned out bowler Marco Jansen had overstepped.
Kuldeep Yadav (five) got a reprieve when Markram spilled one - a rare aberration in an otherwise impeccable catching masterclass by the fielder.
An undeterred Harmer returned to send down a two-wicket over, bowling Kuldeep with a skiddy arm-ball and then inducing an edge from Dhruv Jurel with Markram making no mistake this time.
Rishabh Pant, leading the hosts in the absence of injured captain Shubman Gill, decided to hit spinner Keshav Maharaj for a four and a six but the fun soon fizzled.
Markram took another catch to remove Pant, who lunged forward to defend a Harmer delivery, which hit the shoulder of the bat and the fielder grabbed the lob in the gully region.
Spinner Senuran Muthusamy ended Sudharsan's 139-ball defiance and India's slim chances of saving the match was practically over when Maharaj had Jadeja stumped.
Harmer's tally of 17 wickets fetched him player-of-the-series award.
"As a team we need to get better and you have to give credit to the opposition because they played better than us," Pant said.
