But a fifth home win in five was harder work than it might have been, because Town, despite dominating possession, were never quite able to put this game to bed.
Top scorer Kachunga claimed his fourth of the campaign after just 90 seconds, and while Town old boy Danny Ward equalised after 34 minutes, Wells put Town back in front on 38.
Both sides had chances thereafter, and it was a relief to home fans in an 18,808 crowd (742 from Rotherham) when the final whistle blew.
LOOK: Huddersfield Town v Rotherham United, 27.09.2016: Match Action from the John Smith's Stadium
Rotherham arrived at the John Smith’s Stadium one place off the foot of the table with just one win in all competitions and victorious in only one of their 16 previous meetings with Town.
This 10th league match of the campaign pitted one Danny Ward, the home side’s on-loan Liverpool keeper, against another, the visitors’ former Town frontman.
Town boss David Wagner had to contend with one-match suspensions for skipper Mark Hudson, his fellow defender Chris Lowe and wideman Rajiv van La Parra.
Sean Scannell came in for van La Parra, with Wagner trying to find a way through the division’s most porous defence (22 goals conceded in the nine games beforehand).
There was also a change in midfield, with experienced Dean Whitehead, who rejected a transfer to Rotherham during the close-season, replacing Jonathan Hogg.
Town made a flying start, with their opening onslaught bringing Kachunga’s close-range opener just 90 seconds into the contest.
WATCH: Huddersfield Town players celebrate with the fans after the 2-1 win over Rotherham United
Rotherham were reeling, and both Homes-Dennis and Aaron Mooy had shots blocked as Wagner’s side tried to take advantage.
The team chief was encouraging his players from the touchline as they set about the Millers with real gusto.
Rotherham were working hard to respond, and striker Ward showed some eat footwork, but centre-back Christopher Schindler came to Town’s rescue.
Town were soon back on the offensive and Wells, having earlier produced a lovely flick to create another attack which was finally snuffed out, shot narrowly wide on 15 minutes.
Then the two Wards went head to head, with the town stopper getting there first to collect from the Rotherham man.
Ward was the visitors’ liveliest performer early on, and he won a 24th-minute corner taken by Joe Newell, but it came to nothing.
As Town once again took control, Tommy Smith teed up Scannell, but his drive was deflected away.
The crowd were on their feet as Kasey Palmer broke forward and set up Kachunga one on one with keeper Lee Camp, but the forward was flagged offside.
Then it was Town’s turn to be rocked as Rotherham leveled on 34 minutes, with Ward flicking home Jon Taylor’s cross from the right.
It was his fifth goal of the season, but it scarcely reflected the pattern of play as Town had been by far the brighter up to that point.
Normal service was soon resumed, however, as Scannell’s run and pass freed Wells, who shot home neatly into the left-hand corner in front of the South Stand.
Hefele met a Palmer free-kick, but his effort was straight at Camp, and Rotherham must have been relieved to reach half-time with the scoreline just 2-1.
Town forced a string of corners at the start of the second half, but the visiting keeper dealt with them well.
Lee Frecklington fizzed a 57th-minute shot narrowly wide in a reminder that Rotherham remained dangerous and Town, despite bossing the game, were only one ahead.
Palmer linked neatly with Kachunga, but the on-loan Chelsea forward’s shot was well off target, then Hefele had a header blocked before shooting wide from the rebound.
Frecklington had another shot blocked before Kachunga led a a Town charge on the counter, only to be fouled by Joe Newell.
Town survived a late scare when Adeymi set a header wide with the goal gaping at his mercy.