Hazlewood was preferred to Pat Cummins as Australia's third specialist pace bowler and responded with four for 35 in his 10 overs as the co-hosts beat Pakistan by six wickets at the Adelaide Oval to set up a last four meeting with India.
"There's always pressure in a quarter-final in a World Cup," he told reporters in Adelaide.
"(But) I guess there's a little bit added there, knowing you have to impress to play again. But it could have been our last game playing for everyone."
Hazlewood was replaced by spinner Xavier Doherty for Australia's match against Sri Lanka and when Cummins came in and took 3-42 in the final pool game against Scotland, the 24-year-old feared his tournament was over.
"Those thoughts do run through your head. You try to stay positive," he added.
"It's been obviously a toss of the coin job for most of the tournament between me and Pat. We’ve got the nod in different spots, in different conditions so it was good to get another game to hopefully impress.
"I was just happy to play tonight and contribute to the win."
Hazlewood took his wickets in three different spells and after such strong performance would appear to have nailed down his position in the side for next Thursday's semi-final against India at the Sydney Cricket Ground.
"I hope I've gone a long way to doing that but you never know with the conditions at the SCG," he said. "They could be dry and suit the spinner so you never know but you've just got to try and take your opportunities."
Hazlewood got his second international five-wicket haul with 5-68 in the second test against India at the Gabba last December and 2-25 in a 50-over World Cup warm-up match against the world champions last month.
(Writing by Nick Mulvenney in Sydney, editing by Amlan Chakraborty)
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