Ieremia closed with back-to-back even-par rounds of 71 to finish the Australian Open tied for fifth on eight-under, seven shots behind local victor Matt Jones.
The former Sydney local took the lead at the conclusion of the second round and has held steady since to win by just one shot over Louis Oosthuizen.
Matt Jones moved a step closer to winning the Australian Open for a second time after extending his lead to three strokes at the end of the third round.
South African Oosthuizen, one of six players from the global team who came to Sydney to warm-up for next week's Presidents Cup, mixed three birdies with one bogey in a solid round.
Champion in 2015 on the same course where he's been a member since he was 15, Jones finished at 15-under par for the tournament after closing with a 69.
"I wanted to be aggressive today but it was hard with the pin placements, so I played a little bit safer", he said.
"It doesn't matter if you're four in front or four behind, you're not going to win a tournament of this calibre against a field like this without playing really good golf".
Amateur Takumi Kanaya (71) and Aaron Pike (69) finished tied for third at nine under, while Paul Casey (72), Greg Chalmers (67), Denzel Ieremia (71), Cameron Tringale (73) and Chun-An Yu (67) were a shot further back.
Matt Jones is heading to this third Open Championship courtesy of qualifying at the Aussie Open.
Jones, Kanaya and Pike qualified for next year's British Open by finishing among the top three who were not already qualified.
The Open will be held July 16-19, 2020, as it returns to Royal St. George's for the first time since 2011.
"It's unbelievable, if there is a Major that I would like to win is (The Open)", said Jones, who played at Royal Troon in 2016 and Carnoustie in 2018.
"I'm going to go off and have some dinner then go straight to bed for some rest". "To be able to do that and plan a schedule around that, will be fantastic", Jones said.
Takumi Kanaya makes his birdie on the 72nd hole to book a place in The Open.
Leishman sprayed his approach into the deep rough right, chopped out to the cart path and came up short before two-putting to fall six shots off the pace.
Oosthuizen teamed up with fellow South African Branden Grace in 2015 to become the only global pairing to earn four points in a single Presidents Cup and has a 7-5-3 win-loss-tie record in the biennial competition.
He shot 71 to finish in a share of 10th at seven under.
Their team captain, Ernie Els, missed the Australian Open cut, giving him some extra time to prepare for the four-day tournament against a United States team that has only lost once previously - at Royal Melbourne in 1998.