After dismissing Australia for 473, the highest first innings total in women's test history for a team batting first, England were 218/2 at stumps with Tammy Beaumont leading the charge on an unbeaten hundred.
Beaumont also made full use of the flat pitch to pile on the runs, becoming only the second Englishwoman after Heather Knight to score a century in all three formats.
"I hadn't even thought about it! Heather said, 'Welcome to the club', it hadn't even crossed my mind," Beaumont told the BBC.
"I think it's finely balanced. I think it's a very good batting wicket... I don't think I batted my best, I was stubborn, which Heather has called me for years."
Australia all-rounder Ellyse Perry missed out on her own test century by one run on a rain-hit first day but Sutherland, who was unbeaten on 39 on Thursday, picked up where she left off to guide her team to a commanding total at Trent Bridge.
After losing overnight partner Alana King, who was bowled by an inswinger from Lauren Bell, Sutherland was joined in the middle by Kim Garth before she brought up her century with a flick to the deep midwicket boundary.
FASTEST HUNDRED
Her 148-ball hundred was also the fastest by an Australian woman, breaking a 39-year-old record held by Jill Kennare with a 156-ball century versus England.
"I hope to get up the order. I've been telling the coach that for a little while. I'm just happy playing my part in this team ... it's just about slotting in," Sutherland told Sky Sports at lunch.
However, she ran out of partners when England spinner Sophie Ecclestone cleaned up the tail to finish with a five-wicket haul (5-129) after bowling nearly 47 overs.
Sutherland was not done yet and struck in her first over to dismiss Emma Lamb, luring the England opener into a stroke to edge the ball to Jess Jonassen in the slips for a low catch.
Australia struggled to make a breakthrough after the first wicket as Beaumont and Knight chipped away at the mammoth total and stitched together a 115-run stand.
But as daylight faded and the stadium lights were switched on, Ashleigh Gardner dismissed Knight for 57 when the England skipper was caught behind.
Nat Sciver-Brunt joined Beaumont and, as if inspired by the men's fearless 'Bazball' approach, scored at almost a run a ball, smashing seven boundaries to finish day two on 41 not out.
