
Murray is seeking to end Djokovic's l22-week reign at the top, but the Briton was pushed to the limit by Verdasco in the French capital before prevailing 6-3, 6-7 (5/7), 7-5.
The second seed raced through the opening set but was forced into a decider after Verdasco, who had lost in the first round in five of his past six tournaments, levelled in a tie-break.
The Spaniard then saw two break points pass him by at 5-all in the third set, with Murray breaking the following game to finally end Verdasco's resistance.
"It wasn't the best match from my side. I got through it. I will play better tomorrow," said Murray after sealing his 70th win of the season.
"I didn't get any time on that court, because matches are from 11:00 in the morning and guys have warmup. So I have hit for like 45 minutes on the court beforehand, and it's very different to last week, very different conditions."
Murray, a winner in Beijing, Shanghai and Vienna in his past three events, will continue his assault on Djokovic when he faces Lucas Pouille for a place in the quarter-finals.
Djokovic, the record four-time champion, marched into the third round with a 6-3, 6-4 victory over Luxembourg's Gilles Muller.
The Serb needed four set points before claiming the opener, with Djokovic then breaking at 4-all in the second to extend his Paris winning streak to 16 matches.
"It was great to start off the way I did today," said Djokovic.
"Not an easy opponent, definitely, because he serves and volleys, and I found the conditions quite quick, quicker maybe than they have been last year.
"But nevertheless, I think I managed to find the right rhythm, right pace from the very beginning."
Djokovic -- winner of the last three editions of this tournament -- will meet 14th seed Grigor Dimitrov on Thursday.
The 29-year-old must reach the final in Paris to guarantee he extends his stay at number one with Murray rapidly closing in on the Serb.
- Wawrinka beaten -
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Third seeded Stan Wawrinka, the US Open champion, squandered a match point in the second set tiebreak to lose 3-6, 7-6 (8/6), 7-6 (7/1) to German qualifier Jan-Lennard Struff.
World 91 Struff will face America's John Isner for a place in the quarter-finals.
Stan Wawrinka / AFP
Dominic Thiem faces an anxious wait to see if he qualifies for the World Tour Finals in London after slumping to a 6-2, 6-4 defeat against Jack Sock.
Thiem entered this week's tournament occupying one of the final two qualifying spots for London, but his second-round exit has left his place in the eight-man field vulnerable.
The Austrian dropped his opening service game against Sock, setting the tone for a dismal afternoon as the American blew away the sixth seed in under an hour.
Thiem has won four titles this season and reached the semi-finals of the French Open, but his subsequent dip in form could prove costly with five players still fighting for the remaining two London berths.
Marin Cilic, a winner in Basel at the weekend, further bolstered his chances of playing at the November 13-20 event by defeating compatriot Ivo Karlovic 7-6 (9/7), 6-2.
With Rafael Nadal calling an early end to his season, the Croat is eighth in the Race to London standings and will face David Goffin for a place in the quarter-finals.
Belgian Goffin is still in the hunt after beating Nicolas Mahut 7-6 (9/7), 6-2, while 2008 Paris champion Jo-Wilfried Tsonga cruised past Albert Ramos-Vinolas 6-3, 6-4.
However, Roberto Bautista Agut's London bid ended as the Spaniard squandered three match points before going down 2-6, 6-1, 7-6 (8/6) to Gilles Simon.
The Frenchman plays Tomas Berdych next with the Czech looking to return to the Tour finals for a seventh straight year.
Japanese fifth seed Kei Nishikori collected his 300th career win by knocking off Serbia's Viktor Troicki 6-2, 7-5 to take his place in the last 16.