Maxwell hit a chancy 37-ball 52 with four boundaries and two sixes but could not score the 23 runs required in the final over as Australia -- chasing 148 to win -- ended up at 136 for 8 in their 20 overs.
Pakistan were lifted to 147 for 6 by Babar Azam (45) and Mohammad Hafeez (40) after Sarfraz Ahmed won the toss and opted to bat.
Pakistan won the first match by 66 runs in Abu Dhabi. The third and final match is also in Dubai on Sunday.
The win is skipper Sarfraz's 10th T20I series win since taking over as captain in September 2016, including a tri-series win in Zimbabwe in July this year.
Australia were once again derailed at the outset with D'Arcy Short run out for two in a controversial manner with replays showing he had grounded the bat but was given out by television umpire Riaz Rashid.
Skipper Aaron Finch (3) and big hitter Chris Lynn (7) failed for a second match running as Australia were struggling at 31-3.
Maxwell, dropped thrice on 18, 34 and 52, then added 30 for the fourth wicket with Mitchell Marsh (27) but Pakistan continued to take wickets to keep the Australian chase in check.
When Marsh and Ben McDermott (3) fell in quick succession Australia were in danger of falling to another under-100 total but Maxwell and Nathan Coulter-Nile fought hard during their 59-run seventh wicket stand.
When Shaheen Shah Afridi started the last over Australia needed 23 to win. Coulter-Nile hit a towering six off the first ball and then took a single but Maxwell holed out off the next ball to end all hopes of an Australian win.
Shaheen took 2 for 35 while spinner Shadab Khan finished with 2 for 30.
Pakistan's total was built around a solid 70-run partnership between Azam and Hafeez who built the innings after Fakhar Zaman was out for 11 with the score at 29.
Azam hit three boundaries in his 44-ball knock while Hafeez was in a more punishing mood, smashing two sixes and three boundaries off 34 deliveries.
Shoaib Malik, who came in for Hussian Talat in the team, made 14 while Faheem Ashraf made 17 not out.
Coulter Nile was the best Australian bowler with 3 for 18 while Billy Stanlake took 2 for 36.
australiaBabar AzamBilly StanlakeGlenn Maxwellimad wasimmohammad hafeezNathan Coulter-Nilepakistanpakistan vs australia 2018Shadab KhanShaheen Afridi
First Published: October 27, 2018, 6:43 AM IST