The 38-year-old veteran, playing for Durham, achieved the landmark by bowling out Hampshire for 115 in their first innings, finishing with figures of 10-47 off 17.3 overs.
Durham had made 252 in their first innings of the match being played at Chester-le-Street.
Gibson, who becomes the 79th bowler in first-class cricket history to achieve the feat, is the first since former Indian paceman Debasish Mohanty in 2000-01, and first in county cricket since Richard Johnson took 10 for 45 for Middlesex in 1994.
He reached the mark when he bowled James Bruce for a first-ball duck.
Scores on Sunday:
County Championship (third day of four):
Division One:
At Riverside: Durham 252 (D.M. Benkenstein 114, B.J. Harmison 66; D. Griffiths 4-46, A.D. Mascarenhas 4-33) and 114-2 (M. Stoneman 50); Hampshire 115 (M Brown 56 not out; O.D. Gibson 10-47).
At Canterbury: Kent 550-9 declared (M. van Jaarsveld 117, G.O. Jones 105, Yasir Arafat 101 not out, N. Dexter 86); Warwickshire 107 (R. McLaren 5-24) and 187-5 (D.L. Maddy 115 not out).
At Headingley: Yorkshire 307 (A. Rashid 91 not out, A. McGrath 72; M.J. Nicholson 4-85); Surrey 87-3.
Division Two:
At Derby: Glamorgan 298 (D.L. Hemp 97, G. Rees 51) and 19-1; Derbyshire 150-3 declared.
At Leicester: Leicestershire 305-2 (J. Maunders 97, H.D. Ackerman 93 not out, T.J. New 56) v Middlesex.
At Taunton: Essex 282 (M. Pettini 73, R.S. Bopara 69; C.L. White 4-28) and 294-6 (R.S. Bopara 126, J.S. Foster 71); Somerset 153 (A.J. Bichel 6-63).—AFP