The pole was Rosberg's fourth in succession and meant that Hamilton, who secured his third championship in Texas last weekend, has not started from the top slot for the last five races.
Ferrari's Sebastian Vettel, who is fighting fellow German Rosberg for second place overall with three races to go, qualified third fastest in front of a passionate crowd who reserved their biggest cheers for Mexican Sergio Perez.
Perez will start the first Mexican Grand Prix since 1992 in ninth place for Force India with every chance of scoring points on Sunday.
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Rosberg said it was "business as usual" after beating Mercedes team mate Lewis Hamilton to pole position.
German Rosberg will hope Sunday's race breaks a bitter sequence after converting only two of his last 10 poles into victory. Triple world champion Hamilton has won the last three from second place.
The Briton, who clinched his third championship in Texas last weekend, will again start alongside on the front row with every intention of winning in front of what promises to be a huge and lively crowd.
"It's a good start for sure, starting on pole," said Rosberg. "It's going to be a long run down to turn one so it's going to be an exciting battle and then I'm sure we have a good race car."
Asked whether the pole was 'Angry Nico' fighting back, he shook his head: "Definitely not. There's no difference, it's attack like always.
"It's three more races to go, great to be here in Mexico, great track, I really enjoy driving here so business as usual."
The pair banged wheels into the first corner in Austin, with Rosberg losing out, and Ferrari's Sebastian Vettel was clearly hoping for more fireworks at the Autodromo Hermanos Rodriguez.
"Can you make sure you take both of you out so I can go through?", joked Vettel, who qualified third, to a stony silence from the Mercedes duo.

Lewis Hamilton (Mercedes) - GP of Mexico 2015

Image credit: Daimler AG

The Ferrari driver is second in the championship, after winning three races this season, but is only four points ahead of Rosberg who now has 20 career poles.
"In the end they were just a sniff too quick but who knows what happens tomorrow?," said Vettel.
Hamilton, who has failed to qualify fastest in his last five races after previously racking up 11 out of 12, had hoped to take his 50th career pole but some small mistakes when it mattered ruled that out.
"We have quite a bit of a different set-up this weekend so perhaps the avenue I went might not be the perfect one for qualifying but it'll be good for the race," said the Briton whose team have already retained their constructors' title.
Hamilton is also gunning to equal Vettel's record of 13 wins in a season, having won 10 so far.
The passionate crowd will be reserving their biggest cheers for Mexican Sergio Perez who will start his country's first grand prix since 1992 in ninth place for Force India with every chance of scoring points.
Russian Daniil Kvyat joined Vettel on the second row for Red Bull, with Australian team mate Daniel Ricciardo fifth and Finland's Valtteri Bottas sixth in a Williams.
Teenage Dutch rookie Max Verstappen, fourth in Austin, qualified an impressive eighth for Toro Rosso.
At the back, McLaren's Jenson Button failed to take part in qualifying due to engine problems that are likely to increase his already meaningless 50-place penalty on a grid of just 20 cars.
Team mate Fernando Alonso will join him at the back after qualifying 16th but having a 10-place penalty. Ferrari's Kimi Raikkonen has a five-place drop from 15th.
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