Djokovic would have ceded top position to Rafael Nadal in the event of a defeat - and will still drop to second if the Spaniard goes on to reach the Beijing final, irrespective of his own performance.
Djokovic edged the first set 7-5 against the experienced Verdasco but was distinctly out of sorts in the second as he was broken twice, enabling his opponent to level the scores.
The Serbian raised his game in the decider, breaking Spain's Verdasco twice and saving a solitary break point on his own serve to run out a 7-5 2-6 6-2 winner in one hour and 54 minutes.
Djokovic will play Sam Querrey in the quarter-finals after the American upset Switzerland's sixth seed Stanislas Wawrinka 6-3 7-6 (7/2) in 76 minutes.
Serena Williams recovered from a break down in both sets to claim a 7-5 7-5 win over battling Russian Maria Kirilenko in the women's third round.
Kirilenko, who had lost all seven of her previous meetings with Williams, served for the first set at 5-4 and also led 4-2 in the second before Williams fought back to book a quarter-final place.
Third seed Agnieszka Radwanska beat Slovenian qualifier Polona Hercog 6-0 6-2 to book a last-eight meeting with Germany's Angelique Kerber, who overcame Italian Roberta Vinci 6-2 6-4.
Eighth seed Jelena Jankovic needed just 59 minutes to score a rare double-bagel 6-0 6-0 win over Spain's Carla Suarez Navarro.
The Serbian will next face Czech Lucie Safarova who beat Andrea Petkovic of Germany 6-4 6-7 (4/7) 7-6 (7/2).