The Proteas bowled the visitors out for 80 to seal a convincing 332-run win in the second and final Test at St George’s Park in Gqeberha, formerly known as Port Elizabeth.
Left-arm spinner Maharaj picked up 7-40 and off-spinner Harmer took 3-34 as Bangladesh folded early on the fourth day. They were 27-3 overnight and South Africa needed only another 14 overs to finish the game off, in scenes similar to the first Test where the Proteas spinners also took all 10 wickets in the second innings in dismissing the Tigers for 53.
The hosts had set Bangladesh a huge victory target of 413.
South Africa were always in control after making 453 batting first and restricting Bangladesh to just 217 in the first innings.
However, it was a challenging start to the day as South Africa began with two substitutes in their side after opening batsman Sarel Erwee and all-rounder Wiaan Mulder tested positive for Covid-19 overnight.
The International Cricket Council allows for players to be replaced under such conditions and Khaya Zondo was therefore handed his Test debut, while seamer Glenton Stuurman came in for Mulder.
South Africa won the first Test in Durban by 220 runs, and will be especially pleased with their effort as six of their first team regulars chose to play in the Indian Premier League and were not available, including their entire frontline pace attack of Kagsio Rabada, Anrich Nortje, Lungi Ngidi and Marco Jansen.
"Playing this series with what people have called a weakened squad gives other guys opportunities at this level," captain Dean Elgar said at the post-match presentation.
"Having the luxury of two quality spin bowlers in our squad is brilliant. We have tough challenges coming up, England [July-September] and Australia [December-January] away but if you have a lot of options you give yourself the best chance of winning."
It was not a total failure for Bangladesh as they won the preceding ODI series 2-1 last month. That was the first time the Tigers had won any kind of series in South Africa.
"I'm a bit disappointed but we have to move forward," Bangladesh captain Mominul Haque said. "We could not make partnerships with the bat or ball. We can't give any excuses about the conditions.
"We have to play according to our process and in this series we lost our process."