When Azam reached 48 he completed the landmark in just 26 innings, beating the previous record set by India's Virat Kohli who reached 1,000 runs in 27 Twenty20 innings.
Azam finished with a 58-ball 79 with two sixes and seven boundaries while Mohammad Hafeez scored a 34-ball 53 after Pakistan won the toss and chose to bat at Dubai stadium.
Pakistan defeated New Zealand by 47 runs in the third and final Twenty20 international in Dubai on Sunday to claim another clean-sweep in the game's shortest format.
Leg-spinner Shadab Khan took 3-30 as New Zealand were bundled out for 119 in 16.5 overs.
Pakistan won the first match in Abu Dhabi by two runs and the second by six wickets in Dubai.
First Published: November 5, 2018, 12:33 AM IST