The former world number one, who gave birth to her first child in February of last year, outplayed the former Wimbledon runner-up in one hour, 22 minutes.
Bartoli had won her previous tournament in Stanford, California, but was shocked by Clijsters' early onslaught.
The Belgian dropped just five points as she charged to a 4-0 lead and though Bartoli hit back to level at 4-4, Clijsters broke two games later to take the opening set. After saving two break points in the third game of the second set, Clijsters broke to lead 3-1 and held her nerve to set up a meeting with Patty Schnyder of Switzerland.
Earlier, Ana Ivanovic and Victoria Azarenka fended off tough opposition to reach the second round. Former French Open champion Ivanovic recovered from a poor start to beat American teenager Melanie Oudin 2-6, 6-1, 6-1 while ninth seed Azarenka saw off Kaia Kanepi of Estonia 6-3, 7-6. Former world number one Ivanovic had trouble with her ball toss early on but recovered her composure to storm back in the next two sets.
Ukrainian qualifier Kateryna Bondarenko set up a meeting with second seed Serena Williams after she crushed Magdalena Rybarikova of Slovakia 6-2, 6-2.
Rafa returns
Rafael Nadal's tender knees passed their first test when the Spaniard returned to action on Monday in a doubles win at the Montreal Masters.
Sidelined for more than two months with tendonitis in both knees, Nadal looked fighting fit as he teamed up with coach Francisco Roig to beat Serbian duo Novak Djokovic and Dusan Vemic 7-5, 6-4. "It's great to be back and I had a lot of fun playing with Francisco," Nadal told reporters. It was a positive first step in what is expected to be a testing comeback for the 23-year-old Spaniard, who opens the defence of this Montreal crown with a second round clash against either compatriot David Ferrer or Serb Viktor Troicki.
Roger Federer, who celebrated his 28th birthday last Saturday, opens his Montreal bid on Tuesday against Canadian hope Frederic Niemeyer, who reached the second round with a 7-5, 6-1 win over Russian Igor Kunitsyn. In other first round action, ninth seed Gilles Simon crushed Canada's Frank Dancevic 6-1, 6-2 in a rain-interrupted match to lead a parade of Frenchmen into the second round. Thirteenth seed Gael Monfils made a winning return from a two-month injury layoff battling past former-champion Marat Safin 6-2, 3-6, 6-2.
Jeremy Chardy also advanced, rallying past Taiwan's Lu Yen-hsun 6-7, 6-3, 6-4 to set up a second round meeting with world number three Andy Murray. Paul-Henri Mathieu outlasted Spain's Guillermo Garcia-Lopez 7-5, 0-6, 6-1 while Germany's Rainer Schuettler beat Florent Serra to spoil an otherwise perfect day for the French contingent.
