Clijsters, the 2005 US Open champion, lost serve three times but broke Kuznetsova five times.
'A lot of credit to her,' said the Belgian. 'She started hitting a lot of winners and hitting the ball deep and powerful, and some really good serves where I felt pressure straightaway in the beginning of rallies.'
Clijsters worked upon her desire to get back into the sport after resuming training for an exhibition series she played last May to mark the debut of the new Wimbledon centre court roof.
The Belgian, winner of 45 singles titles, announced her comeback effort five months ago.