Hajsafi's swift control and scything strike from the corner of the box raised the roof at Melbourne Rectangular Stadium as Team Melli opened with a pulsating 2-0 win.
Earlier UAE's top-rated midfielder Oman Abdulrahman bewitched Gulf rivals Qatar in a 4-1 rout achieved through braces to both Ahmed Khalil and Ali Mabkhout in Canberra.
UAE went behind to "Qatari Maradona" Khalfan Ibrahim's sweetly executed volley before they roared back to put a huge hole in the campaign of the 2022 World Cup hosts.
Bahrain's Nigerian-born striker Jaycee Okwunwanne blazed just wide and Sayed Shubbar headed a golden opportunity over as Bahrain threatened to capitalise on Iran's sluggish start.
But with nearly the last kick of the first half, Hajsafi struck when he juggled a clearance from his left to his right boot and smashed it into the top corner.
Okwunwanne knocked Iran 'keeper Alireza Haghighi backwards with a ferocious drive before Masoud Shojaei popped up to steer home a mishit effort from a corner.
"We deserved one more goal. But to play against Bahrain is difficult."
He added: "The game dictates that the team that controls the game, the best team on the pitch, won today. So we start to move forward, rest, and I think our next game Qatar will be a decisive game for both teams.
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