Australia’s Glenn Maxwell produced an unbeaten half-century in a tense chase to help the hosts edge out South Africa by two wickets in the third and final T20 international in Cairns on Saturday.

Maxwell’s unbeaten 62 off 36 balls helped Australia chase down a 173-run target with one ball to spare in a thrilling decider at the Cazalys Stadium, completing a 2-1 series victory in style.

After 18 overs of their innings, it was a run-a-ball target for Australia with Maxwell in the middle. The South African bowler Corbin Bosch (3-26) claimed two wickets in the penultimate over and kept Maxwell away from the strike. Needing 10 off the last over from Lungi Ngidi, Maxwell took six from the first four balls before reverse-sweeping the bowler for a four to seal Australia’s dramatic victory.

“It was a little bit nerve-wracking,” Maxwell said after being awarded player of the match. “I probably had to do the majority of the striking but, yeah, it was nice to get a couple out of the middle right near the end.”

Put in to bat, South Africa overcame a top-order wobble to post a competitive 172-7 with Dewald Brevis (53) top-scoring for them. The tourists were 49-3 inside seven overs but Brevis looked unfazed and hit Aaron Hardie for four sixes in an over, throwing the pacer out of the attack.

Dewald Brevis top-scored for South Africa with 53 off 26 balls. Photograph: Saeed Khan/AFP/Getty Images

Brevis raced to a 22-ball fifty but Maxwell took a brilliant running catch near the rope to dismiss him off the bowling of Nathan Ellis (3-31). Tristan Stubbs contributed 25 and Rassie van der Dussen made 38 not out down the order but South Africa still fell just short of the 175 mark.

Skipper Mitchell Marsh (54) led Australia’s robust reply, dominating his 66-run opening stand with Travis Head (19). Kagiso Rabada floored a return catch from Marsh when the batter was on 26 and Aiden Markram gave a similar reprieve to Head off his own bowling. Head could not capitalise on it though, falling to Markram in the same over.

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Bosch bowled Josh Inglis for a first-ball duck before South Africa’s teenage left-arm quick, Kwena Maphaka, dismissed Marsh and Cameron Green (nine) in the same over to turn the match on its head.

Rabada also produced a two-wicket over, dismissing Tim David (17) and Hardie but Maxwell stayed calm to guide Australia home. The three-match one-day international series between the sides begins in Cairns on Tuesday.