Murray becomes No. 1 if he wins the tournament and Djokovic – winner for the past three years – does not reach the final.
Djokovic began his quest for a fourth straight Paris Masters title by easing past Luxembourg’s Gilles Muller 6-3, 6-4.
Murray is full of confidence after three straight tournament wins, but needed to scrap hard to beat Verdasco 6-3, 6-7 (5), 7-5.
Murray’s 12th win in 13 career matches against the Spaniard was unconvincing and he needed 2 ½ hours to prevail.
“I didn’t feel that comfortable,” Murray said. “The match wasn’t played on my terms. He was dictating the points.”
It was scrappy stuff as they conceded 25 break-point chances between them.
“It wasn’t the best match,” said Murray, who next faces 13th-seeded Frenchman Lucas Pouille. “I will play better tomorrow.”
U.S. Open champion Stan Wawrinka will not get that chance.
The third-ranked Swiss lost to Germany’s Jan-Lennard Struff 3-6, 7-6 (6), 7-6 (1), letting Struff off the hook when he failed to convert a match point at 6-5 in the tiebreaker.
There was no such drama for Djokovic.
Celebrating his win several hours earlier, he tapped his hand against his heart and made a throwing gesture to all four sides of the court as if to share the moment with the crowd.
Djokovic has a special bond with Paris, also winning this tournament in 2009 and clinching the French Open in June to complete his collection of all four majors.
Djokovic saved the only break point he faced in the second set and was clinical when it mattered.
With the score 4-4 and 30-40, Muller sent down a strong serve that Djokovic returned with venom. It surprised Muller, who swatted a forehand into the net.
The Serb sealed victory on his first match point with an ace straight down the middle.
He next faces Grigor Dimitrov in the third round and has a 5-1 career record against the 14th-seeded Bulgarian, while Murray leads Pouille 2-0.
Pouille earlier advanced by beating Spaniard Feliciano Lopez 6-7 (1), 6-3, 6-4.
“He’s a big hitter,” Murray said about Pouille. “He takes chances.”
Murray moved 4-2 up in the second set against Verdasco. But after the Spaniard leveled the match in a tense tiebreaker, Murray swiped his racket angrily through the air and then yelled at himself when he sat down.
His frustration was not over.
Murray broke to lead 2-0 in the deciding set, but Verdasco held on.
Finally, Murray broke him to love in the 12th game to win.
Wawrinka was out of sorts in his clash. In the first set, he made 20 unforced errors and gave nine break-point chances, but Struff failed to convert any of them.
When Struff eventually broke Wawrinka in the seventh game of the deciding set – at the 14th attempt – Wawrinka tossed his racket to the ground.
Serving for the match at 5-4, Struff returned the favor, double-faulting to hand Wawrinka a reprieve.
But Wawrinka fell apart in the tiebreaker as Struff advanced to meet big-serving American John Isner.
Earlier, fifth-seeded Kei Nishikori of Japan downed Viktor Troicki of Serbia 6-2, 7-5 and next faces 11th-seeded Jo-Wilfred Tsonga, who beat Spaniard Albert Ramos-Vinolas 6-3, 6-4.
David Goffin kept alive his slim chances of qualifying for the season-ending ATP finals in London by defeating Nicolas Mahut 7-6 (5), 6-3.
Ninth-seeded Marin Cilic can also still qualify for London and he won 7-6 (7), 6-2 against Ivo Karlovic.
Isner had 12 aces in a 7-6 (4), 7-6 (4) win against 15th-seeded David Ferrer. It was his second win in nine matches against the Spaniard, and both have been here.
In other second-round matches, American Jack Sock beat sixth-seeded Dominic Thiem 6-2, 6-4; Gilles Simon downed Roberto Bautista Agut 2-6, 6-1, 7-6 (6); and No. 16 Pablo Cuevas won 6-1, 6-2 against Paolo Lorenzi.
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