The win by the seventh-seeded Raonic means the 23-year-old from Thornhill, Ont., keeps alive his hopes of qualifying for the ATP finals.
"This match was very important in the sense of just getting my teeth into this tournament, giving myself another chance," said Raonic. "I know I'm going to have to play better.
"Fortunately I felt like I was playing better and better at the end of the match especially."
Raonic would be guaranteed a spot in the season-ending tournament by winning the Paris title, though other scenarios are also possible depending on how his rivals do this week. The Canadian served as an alternate at London a year ago but never took to the court.
Raonic took the match into a deciding tiebreaker and served his way out of danger in the end.
"That thought (of going out of contention with a loss) didn't really cross my mind," said Raonic, whose season could have ended with a loss. "But, that (qualifying for the finals) obviously is a factor. I felt like I did a good job in that tiebreak. I got ahead on one point and then just really took care of my service points."
Raonic pounded down a service winner to yield two match points, converting on the first with a crisp cross-court volley winner.
After beating Sock for the fifth time this season, Raonic credited his serve with seeing him through repeatedly over the American.
"My serve helps me out of a lot of tiebreaks against him," he said. "I think he's playing much better now than he was at the start of the year."
Raonic needed two hours to hold off Sock, who also dropped a 6-1, 6-4 men's doubles decision with Vancouver's Vasek Pospisil. They fell to Stan Wawrinka and Leander Paes, knocking them out of contention for a London berth in men's doubles.
Roger Federer was made to fight all the way by local favourite Jeremy Chardy before reaching the third round, while Andy Murray moved one match away from qualifying for the ATP Finals.
The 17-time Grand Slam champion completed a 7-6 (5), 6-7 (5), 6-4 victory at the Palais Omnisports to keep his challenge for the year-end No. 1 ranking well on track.
Federer could have sealed the win earlier but Chardy, who beat him earlier this year on clay at the Rome Masters, saved two match points at 5-4 in the second set before forcing a decider with a stunning crosscourt forehand winner.
The 33-year-old Federer arrived in Paris undefeated in his past 12 matches on the back of consecutive titles in Shanghai and Basel, trailing top-ranked Novak Djokovic by 490 points.
With 2,500 points up for grabs between Paris and at the ATP Finals in London, Federer is looking to clinch the year-end top spot for a record-equaling sixth time. He will also have a chance to earn points with Switzerland in the Davis Cup final against France next month.
Federer's Davis Cup teammate Stan Wawrinka joined him in the third round after winning his first match in more than a month.
The third-seeded Wawrinka ended a three-match losing streak with a 6-4, 7-6 (6) win over 37th-ranked Dominic Thiem — the youngest player in the top 50 — before Murray dispatched Frenchman Julien Benneteau 6-3, 6-4.
Following consecutive losses in Tokyo, Shanghai and Basel, Wawrinka put on an erratic display but prevailed on the important points.
"I'm trying to find my confidence," the Australian Open champion said. "I know things can change quickly. I can lose first round, and I can also go very far in a tournament."
Wawrinka closed out the match on his second attempt after the 21-year-old Thiem failed to convert a set point at 6-5 in the tiebreaker.
Murray converted all three break points and lost only four points on his first serve to claim a 19th win since losing in the U.S. Open quarterfinals. He will need to beat Grigor Dimitrov in the next round to qualify for the season finale.
Four berths are left in the race to London, with six players, including Raonic and Dimitrov, still in contention to join Djokovic, Federer, Wawrinka and Marin Cilic from Nov. 9-16 at the O2 Arena.
After missing last year's tournament following surgery on his back, Murray is pushing hard to qualify for the indoor event for the seventh straight year. Over the past five weeks, the Scot has won three titles and climbed to fifth in the ATP Race.
"If I get in to London I deserve to be there, because it's your results across the whole year," Murray said. "My results in most of tournaments this year, most of the big tournaments, have been good enough to be in the top eight."
Next up for Raonic is 11th-seeded Roberto Bautista Agut, who defeated former semifinalist Richard Gasquet 6-4, 6-2.
Although disappointed, Gasquet was relieved to be able to turn his attention to the Davis Cup final against the Swiss next month in Lille.
"I will now be 100 per cent focused on the Davis Cup," Gasquet said, "and I'm happy it will be played on clay."
In men's doubles, seventh seeds Daniel Nestor of Toronto and new Indian partner Rohan Bopanna opened with a 6-4, 6-0 defeat of Spaniards Fernando Verdasco and David Marrero. They needed just 50 minutes to complete the victory to move into the quarter-finals.
With files from The Associated Press.