On-loan German forward Kachunga gave David Wagner’s side the perfect start after 86 seconds, poking home his fourth goal of the season from close range in a goalmouth scramble.
Rotherham, who have yet to pick up a point on their travels this season, levelled in the 34th minute as former Town winger Danny Ward stole in at the near post to guide home Jon Taylor’s cross for his fifth goal of the campaign.
The Millers were on terms for just four minutes, however, after Wells turned onto Sean Scannell’s pass and found the net with a low shot off the inside of goalkeeper Lee Camp’s far post.
Defender Michael Hefele almost made it three, but somehow headed his effort straight at Camp from point-blank range.
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Rotherham midfielder Tom Adeyemi then missed the target with a late header as Town closed out the win to leapfrog Norwich at the summit, while the Millers drop to last place on just six points.
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