Despite a fall after two minutes and 13 seconds, he ended the day in sixth place.
Pope had earlier finished seventh in the men's lead semi-finals, climbing 35 metres in his allotted six-minute time frame to secure his qualification spot.
First-ever women’s climbing Olympic gold won by Slovenian favourite Garnbret
The men's standings were led by Czech Adam Ondra, who qualified first, and climbed 45+ in the final to win gold ahead of Alberto Gines Lopez of Spain, and bronze medallist Sascha Lehmann of Switzerland.
Great Britain's other hopefuls failed to qualify, with Will Bosi finishing just outside in ninth place on 33+, and Hamish McArthur finishing 15th with 26+.
In the women's event, Slovenia's Lucka Rakovec put in an incredible climb of 46+, touching the top of the wall before losing grip, but still grabbed gold. Laura Rogora of Italy finished second with Luce Douady of France in third.
Great Britain's Molly Thompson-Smith fell at the last in the semi-final and was knocked out of the qualification spots, eventually finishing 12th.
Anak Verhoeven of Belgium - the final competitor of the morning - topped the qualifying table.
Vladislav Deulin of Russia won gold in the men’s Speed final on Saturday, with Danyil Boldyrev of Ukraine taking silver, and Dmitrii Timofeev of Russia securing the bronze.
Deulin posted the fastest time on the day during the semi-finals, stopping the clock at 5.633. The world record is 5.48 seconds.
On the women’s side of the draw, Aleksandra Miroslaw from Poland took gold, followed by Mariia Krasavina of Russia taking silver, and Anouk Jaubert of France claiming the bronze in the small final.
Sport Climbing W Combined Finals
'He does! He does!' - Huge drama as gold medal changes hands on final climb