The British No 3, ranked 67, struggled in the first set, but hit back impressively to win 1-6, 6-3, 6-3 in an hour and 43 minutes.
Evans was particularly dominant on his first serve, losing only seven points, and a single break in each of the last two sets was enough to topple the world No 37.
Evans will next play top seed Dominic Thiem as he continues his build-up to the Australian Open.
Thiem survived a lengthy tussle with qualifier Gastao Elias to reach the quarter-finals.
Austria’s Thiem was a break up in the opening set but lost it on a tie-break and was pushed all the way in a 6-7 (5/7), 6-3, 7-5 victory that took two hours and 39 minutes.
Two-time defending champion Viktor Troicki extended his winning run in Sydney to 13 matches with a 6-3, 6-4 win over Paolo Lorenzi.
The top six seeds are all through to the last eight.
Second seed Pablo Cuevas and fourth seed Pablo Carreno Busta won three-set battles against Nicolas Mahut and Mischa Zverev respectively, and they were joined by Philipp Kohlschreiber and Gilles Muller.
It was the end of the road, though, for 17-year-old Australian Alex De Minaur, who retired through injury after losing the opening set 6-2 to Andrey Kuznetsov.
In New Zealand, there was defeat for British No 8 Brydan Klein in the second round of the ASB Classic in Auckland.
Klein posted an excellent victory over Facundo Bagnis in round one, a player ranked 269 places higher, but Joao Sousa proved too strong, the Portuguese winning 6-3, 6-4.