The 19-year-old, who was named WTA Newcomer of the Year in 2016, has struggled to maintain her momentum this year, failing to get past the third round in all but one of her competitions, a quarter-final loss at the Auckland Open in January.
Osaka missed the SW19 event last year due to injury but is confident she can excel on grass despite recording 40 unforced errors against Tormo.
"I think we can say that I play well on grass," Osaka told reporters after the match.
"I'm quite upset with my stats. I felt like crying when I wasted a match point (up 6-5 in the second set) but I pulled myself together and focussed once again."
Osaka will continue her Wimbledon campaign against Czech 22nd seed Barbora Strycova in the second round on Wednesday.
(Reporting by Aditi Prakash in Bengaluru; Editing by John O'Brien)
