Federer, ranked second in the world, prevailed against eighth-ranked Raonic 6-1, 7-6.
After easing through the first set, the Swiss star struggled in the second set before decisively winning a tie-breaker 7-0 to win the second.
The hard-serving Raonic knocked Federer out of the quarterfinals of the Paris Masters last week.
"I was very happy with how I performed," Federer said.
"The second set was much tougher," he acknowledged.
"I don't think he played a great breaker but it was a great one to win," Federer said.
"It's a small relief," he added.
"We have a tough group here so it's always going to be hard advancing but it brings me a step closer."
At 33, Federer has been in age-defying form this year and he arrived as the oldest player to qualify for the tournament in his record 13th consecutive appearance.
Federer is set to become the oldest player to finish a season in the world's top two and still has a slim chance of becoming the oldest player to end the season as world number one if he overhauls Serbian Novak Djokovic in the race for top spot.
The Basel native next faces Japan’s Kei Nishikori who eliminated Scotsman Andy Murray 6-4, 6-4 in Group B.
Federer last won the prestigious season-ending event at London's O2 Arena in 2011.
On Monday, fellow Swiss and Australian Open champion Stan Wawrinka plays Tomas Berdych from the Czech Republic, while defending champion Djokovic faces US Open winner Marin Cilic, from Croatia.