Anil Kumble (619) and Kapil Dev (434) are the other two Indian bowlers to have recorded the feats.
Playing in his 96th match, Harbhajan achieved the feat when he bowled Carlton Baugh on the second day of the third and final cricket Test against the West Indies here.
Harbhajan, who made his Test debut against Australia in 1998, needed two wickets to reach the landmark at the start of this match, and seven at the start of the three-match Test series.
In March 2001, he proved too much for the all-conquering Australians, collecting 32 wickets in three Tests, including the first Test hat-trick by an Indian. Harbhajan, who got a standing ovation from the balcony and pats from his team-mates on reaching the landmark, has 25 five-wicket and five ten-wicket hauls in this form of the game. Former Sri Lankan off-spinner Muttiah Muralitharan, with 800 wickets, leads the list.