Australia dismissed Zimbabwe for 196 in 48.5 overs and replied with 199 for two, easing to victory by eight wickets with 19.2 overs to spare.
Gillespie took five for 32, his third five-wicket haul in one-dayers, while Clarke scored a career-best 105 not out.
Zimbabwe collapsed to 61 for six before Elton Chigumbura and Mluleki Nkala resurrected the innings with a stand of 114, a seventh-wicket record for Zimbabwe against Australia.
Chigumbura scored 77, his maiden half-century, and Nkala was out for 47.
Australia won the first two matches of the series by seven wickets and 139 runs.
Scorecard:
Zimbabwe
S.Matsikenyeri c Watson b Gillespie 4
B.Taylor lbw b Gillespie 1
V.Sibanda c Gilchrist b Gillespie 2
T.Taibu lbw b Kasprowicz 27
M.Vermeulen c and b Gillespie 17
A.Maregwede b Gillespie 1
E.Chigumbura b Hogg 77
M.Nkala b Hogg 47
T.Mupariwa run out 4
W.Mwayenga lbw b Hogg 1
E.Rainsford not out 1
Extras (lb-5 nb-1 w-8) 14
Total (all out, 48.5 overs) 196
Fall of wickets: 1-4, 2-9, 3-10, 4-42, 5-50, 6-61, 7-175, 8-194, 9-196
Bowling: Gillespie 10-2-32-5 (w-2), Kasprowicz 10-1-27-1, McGrath 8-1-28-0 (w-2), Shane Watson 8-0-38-0 (nb-1 w-2), Hogg 6.5-0-37-3 (w-2), Symonds 6-0-29-0
Australia
A.Gilchrist b Mupariwa 44
M.Clarke not out 105
A.Symonds c Mwayenga b Mupariwa 20
S.Watson not out 18
Extras (lb-4 w-8) 12
Total (for two wickets, 30.4 overs) 199
Fall of wickets: 1-68 2-115
Did not bat:
Bowling: Nkala 5-0-27-0 (w-3), Mwayenga 3-1-22-0, Mupariwa 8-0-48-2, Rainsford 7-0-36-0 (w-4), Matsikenyeri 5-0-35-0 (w-1), Chigumbura 2.4-0-27-0
Result: Australia won by eight wickets, and win the three-match series 3-0.
