The South African scored a robust 130 as his team were restricted to 283 while chasing a stiff 318-run target under lights to concede a 1-0 lead in the three-match series.
Africa were wobbling at 31-5 before all-rounder Pollock led the recovery with a brilliant innings under pressure. He received valuable support from Zimbabwean Elton Chigumbura (40) and Kenyan Thomas Odoyo (39).
Pollock, playing only as a batsman after undergoing a foot surgery recently, gave many anxious moments to the Asian team as he put on 67 for the eighth wicket with Chigumbura and 103 for the next with Odoyo.
The South African reached his hundred in style, hitting Pakistani fast bowler Mohammad Asif for a four. He struck one six and 19 fours in his 110-ball knock.
Asia's total owed much of its substance to Pakistan's Mohammad Yousuf (66) and skipper Mahela Jayawardene (65), who put on 94 for the fourth wicket to prop up the innings.
Yousuf also became the third Pakistani batsman to complete 8,000 runs in one-day internationals during his 74-ball knock after the retired duo of Inzamam-ul-Haq and Saeed Anwar.
Asian pacemen Asif (3-57) and Zaheer Khan (2-43) then raised hopes of an easy victory when they shared five early wickets in their lively opening spells to put Africa under pressure.
But Pollock, who turns 34 next month, made the Asian side struggle for wickets as he batted confidently against both pace and spin before being the last man out.
Africa's batting woes began with the second-ball dismissal of opener AB de Villiers, who was bowled by an Asif delivery that cut in sharply.
Skipper Justin Kemp, Loots Bosman, Steve Tikolo and Boeta Dippenaar then fell in quick succession to leave their team in deep trouble.
Veteran Sri Lankan left-arm spinner Sanath Jayasuriya finished with three wickets.
The Asian batting earlier never looked under pressure as Jayawardene, Yousuf and the Indian trio of Virender Sehwag (45), Sourav Ganguly (32) and Yuvraj Singh (31) made merry on a good batting track.
Debutant seamer Morne Morkel of South Africa was the most successful bowler with 3-68. His brother Albie and paceman Chigumbura grabbed two wickets apiece.
Sehwag and Ganguly had put the Asian side on course for a big total with a brisk 68-run stand for the second wicket off just 49 deliveries.
Jayawardene, who led Sri Lanka to the World Cup final in April, and Yousuf then built on the Indian duo's efforts to ensure the African side chased a stiff target.
The remaining two day-night matches will be played in Chennai on Saturday and Sunday.
Asia XI 317 for 9 in 50 overs ( Mohd Yousuf 66, Jayawardene 65, Sehwag 45, Ganguly 32, Yuvraj 31; Morne Morkel 3 for 68, Chigumbura 2 for 56, Albie Morkel 2 for 64) beat Africa XI 283 all out in 47.5 overs (Shaun Pollock 130, Chigumbura 40, Odoyo 39; Asif 3 for 57, Jayasuriya 3 for 52, Zaheer 2 for 43, Harbhajan Singh 1 for 54) by 34 runs.