The Ford driver was 0.4 seconds quicker than second-placed Sebastien Loeb's Citroen.
The whole top 10 was within 1.9s over the one-kilometre stage, with Mads Ostberg putting his Adapta Ford third, just ahead of Mikko Hirvonen in the second works Citroen, Jari-Matti Latvala's Ford and Ott Tanak's M-Sport Ford.
Chris Atkinson began his World Rally Championship comeback for Monster Ford with seventh place.
Solberg tops Mexico qualifying
The full-length stages commence on Friday morning just after 8am local time.
Monster reveals Atkinson's livery
Latvala admits to crash distraction
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