Sutherland scored a first-class career-best 101 not out to help the Vics to 9-431, declaring immediately upon reaching his second first class ton.
WA finished day two at the WACA on 5-200 in their first innings, with Joel Curtis unbeaten on 26 and Fanning having been dismissed in the final hour for 99.Â
Sutherland gave a perfect exhibition of how to bat with the tail, scoring 70 of their 88 runs on day two.
He reached his century off 139 balls, hitting 14 fours and two sixes.
Sutherland dominated the opening session to such a degree that none of the other Victorian batters on Tuesday contributed a single boundary.
He extended an overnight eighth wicket stand of 30 with Sam Elliott to 71.
Sutherland was still 34 runs off his century when joined by last man Boland.
The Vics skipper then smashed five fours and two sixes to race to his ton, while Boland finished with one off 21 balls.
Paceman Brody Couch and spinner Corey Rocchiccioli each took three wickets.
In his more comfortable role with the ball, Boland then broke an opening partnership of 28 when he had former Test opener Cameron Bancroft caught behind for 11.
Fanning and Jayden Goodwin put on 79 for the second wicket before Sutherland won an lbw decision against the latter.
The metronomic Boland struck 18 runs later, bowling veteran Sam Whiteman.
Fanning added 41 with Teague Wyllie, who was caught in the slips off Elliott, with his partner on 99.
Having eclipsed his previous best first-class score of 95, Fanning fell agonisingly in the next over after striking 12 fours and running with plenty of purpose.
He edged a delivery from Fergus O'Neill, with wicketkeeper and first day centurion Sam Harper taking a fine juggling catch standing up to the stumps.
