Price ripped through the Australian lower-order to finish with career-best figures of six for 121 and restrict Australia to a modest first innings total of 403.
That left Australia with a first innings lead of 95, but Zimbabwe quickly wiped out the deficit before bad played stopped play early at the Sydney Cricket Ground.
However, they spoiled their brave comeback by losing three late wickets to end the day on 151 for four, a lead of just 56 with two full days to go.
Price, the nephew of golfer Nick Price, had earlier brought the Zimbabweans back into the match with his six-wicket haul.
Australia started the day on 245-3, in reply to Zimbabwe's 308, and quickly set about building a lead before Price, a left-arm spinner, suddenly applied the brakes by dismissing the captain Steve Waugh for 61 then his deputy Ricky Ponting for 169.
He had Waugh caught at short leg shortly after the skipper had posted his 48th test half century then removed top-scorer Ponting with a ball that deceived him and rolled off his bat and through his legs on to the stumps.
Australia lost a third wicket before lunch when Zimbabwe skipper Heath Streak bowled dangerman Adam Gilchrist for 20 with a perfect inswinging yorker to claim his first wicket of the series.
Price then returned to mop up the tail after lunch, claiming the scalps of Simon Katich (52), Brad Hogg (13) and Brad Williams (seven) to finish with five wickets for the day and six for the innings, his best return in Test cricket.
Zimbabwe, who lost last week's first test in Perth by an innings and 175 runs, made a terrible start to their reply when opener Dion Ebrahim fell to Williams on the fourth ball of the innings.
But Mark Vermeulen and Trevor Gripped steadied the innings with a second-wicket partnership of 93 before the wheels fell off again despite facing an Australian attack weakened by the absence of all their frontline bowlers.
Vermeulen fell two runs short of a half-century when he was brilliantly caught by Waugh in the covers then part-time spinner Katich chipped in to get rid of Gripper (47) and first innings century-maker Stuart Carlisle (five).
Leading by 19 runs with four wickets already down, Zimbabwe rallied again in the final half hour with Craig Wishart (32 not out) and Tatenda Taibu (13 not out) guiding them through to the early close without any further losses.
