The 36-year-old, who smashed twin hundreds in the first Test, notched 111 not out for his 27th century to help Pakistan close the opening day on a solid footing of 304-2 after they won the toss and batted on a flat Sheikh Zayed Stadium pitch.
In the last over before stumps Azhar Ali also completed his sixth Test hundred and was unbeaten on 101 on a day Australia used as many as eight bowlers and unusual fielding placings but failed to break the Ali-Younis third wicket stand which has so far yielded 208 runs.
England's Herbert Sutcliffe was the last man to score three hundreds in three consecutive Test innings against Australia way back in 1924-25.
Before Younis three Pakistani batsmen Zaheer Abbas (v India in 1982) Mudassar Nazar (v India in 1982) and Mohammad Yousuf (vs West Indies in 2006) had achieved the feat.
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So ruthless was Younis that even the second new ball taken soon after it was due couldn't disturb him. He has so far hit ten boundaries and a six during his 155-ball knock.
Pakistan won the first Test by a big 221-run marging in Dubai.
Younis survived two leg-before reviews, off Maxwell when on 35 and off Steven Smith when on 68.
Ali, who hit six boundaries off 223 balls, too survived two sharp chances, on 34 and 46 suming up a unrewarding day for Australia.
Hafeez fell to an edge behind the wicket off paceman Mitchell Johnson who toiled hard for his figures of 50-1.
Shehzad was shaping well during his 64-ball knock, hitting three fours before he missed a delivery from spinner Lyon and was trapped leg-before.
Clarke juggled his pace bowlers before bringing Lyon on in the 14th over to get the needed breakthrough.
Pakistan, seeking to win their first series against Australia since 1994, kept the same XI while Australia brought in paceman Mitchell Starc and spinning all-rounder Maxwell for batsman Alex Doolan and left-arm spinner Steve O'Keefe, preferring a three-prong pace attack with one spinner in Lyon.