The second seed, who has failed to get beyond the third round in four previous attempts, won 89 per cent of her first serve points on her way to seeing off Tig 6-4 7-6 (7-4) in a time of one hour and 48 minutes.
She had 39 winners to 35 unforced errors and will now take on Ana Bogdan – a 6-1 6-3 winner against Elisabetta Cocciaretto on Sunday – for a place in the last 32.
Osaka, who announced before the tournament that she would not be doing post-match media duties, had just one clay-court victory to her name heading into the second grand slam of the year, but she soon found her groove against world number 63 Tig.
However, after earning an early break of serve, the Australian Open champion squandered three set points in the eighth game as Tig hit back.
Osaka made her superiority show in the following game to take a 1-0 lead in the match and held throughout a tight second set, which went the distance.
Tig, who reached the third round in Paris last year, initially held her own but Osaka pulled away to take the tie-break 7-4 on Court Philippe-Chatrier.