Openers Rizwan (67 off 52) and Babar Azam (39 off 44) shared a 71-run stand before Zaman ended the innings on a high with his unbeaten knock.
The last five overs yielded 59 runs for Pakistan.
Pakistan enjoyed their best powerplay of the tournament, racing to 47 for no loss in six overs after Australia put them in to bat.
Rizwan, who was down with flu ahead of the game, did not look at his best early on and Babar took the lead in attacking the Australian pace attack. The Aussies were looking for some swing early on but they were not able to get it.
The Pakistan skipper began with a regal cover drive off a late outswinger from Josh Hazlewood. Babar, who had shown supreme form in the group stage, looked in sublime touch. Among the five regal boundaries he hit, his short-arm jab between deep midwicket and long-on stood out.
Leg-spinner Adam Zampa, who has been Australia’s go to bowler in the middle overs, finally got the breakthrough Australia needed by having Babar caught in the deep with Pakistan reaching 71 for one in 10 overs. More than the ball, it was the pressure created by Zampa that led to the wicket.
Rizwan, who was dropped twice in the innings, got into the act after Babar’s dismissal. The wicketkeeper batter grew in confidence as his innings progressed and once he he got his trademark half full half sweep shot right off Hazlewood, he looked much more dangerous.
Australia did well from overs 7-11, conceding only 28 before Rizwan changed
He decided to take the attack to the impressive Zampa in the 12th over which went for 14 runs and included a slog sweep for six.
Rizwan got his second six off Hazlewood two overs later, dispatching the seasoned pacer over deep midwicket.
Zaman, who did not have a lot of runs under his belt heading into the semifinal, hit a flat six over long off to gain confidence.
With Zampa completing his tidy effort, Pakistan were looking for a big over and that happened to be the 17th when Hazlewood was hammered for 21 runs, including a six off a free hit.
After Rizwan’s dismissal, Zaman displayed his power hitting skills against Mitchell Starc, clubbing him for a six and four in a 15-run over.
Six-hitting machine Asif Ali had a rare failure in the tournament as he was out first ball off Cummins.
Zaman finished the innings on an exhilarating note, depositing Starc for two massive sixes to take the team past 170.
Zampa (1/22 in four overs) was the pick of the bowlers for Australia while Hazlewood was the most expensive, leaking 49 runs in four overs.