Harbhajan, who is hoping to come back to the Indian side, toiled hard on the opening day of Essex versus Hampshire match on Thursday.
The offspinner bowled 28 overs without success. He bowled three maiden overs and conceded 73 runs.
The first day of the four-day game at County Ground, Chelmsford, saw Hampshire scoring 303 for six wickets in 96 overs.
Hampshire captain Jimmy Adams won the toss and elected to bat first. Former South African opener Neil McKenzie punished Essex bowlers as he remained unbeaten on 134 at the end of the day.
Harbhajan, in his first match for Essex this season, against Gloucestershire, had bowled 13 overs without a wicket for 33 runs.
His hunt for wickets will continue on Friday, on the second day of the match.