Pope was deputising for Jos Buttler, who had X-rays after taking a blow to his left index finger while keeping on day two. Buttler's injury will be evaluated at the end of the Sydney Test, team officials said.
The stand-in took another catch to dismiss Harris off spinner Jack Leach, giving Australia's selectors reason to ponder whether to stick with Harris for the final Hobart Test or keep first-innings centurion Usman Khawaja in the side for Travis Head's likely return.
England earlier added 36 runs before they were dismissed for 294 to give Australia a 122-run innings lead.
Jonny Bairstow added 10 more runs on the fourth morning before he looked to play Scott Boland down to third man only to get an outside edge for wicketkeeper Alex Carey.
The big Yorkshireman soaked up the crowd's applause as he left the field, after his first Ashes century in Australia.
Bairstow faced 158 balls and hit eight fours and three sixes, battling on after taking a nasty blow to his thumb from Pat Cummins when he was on 60.
Boland continued his remarkable series with his team's best figures of 4-36.
Since his extraordinary Test debut in Melbourne, where he was man of the match with 6-7, he has captured 11 wickets at 8.27.