Boucher plundered 78 runs off 38 balls as South Africa hammered 392 for six in their 50 overs after being sent in to bat by Pakistan, who conceded their highest total in one-day internationals.
The home attack then dismissed Pakistan for 228 in 46.4 overs for an easy victory.
Pakistan needed to mount the second highest successful run chase in ODI history, requiring a mammoth 7.86 runs per over, and although they scored briskly, South Africa picked up wickets at regular intervals.
A partnership of 49 off 35 balls between Mohammad Yousuf and Inzamam-ul-Haq lifted Pakistan after Makhaya Ntini plundered the top-order to leave them on 70 for four.
But Yousuf fell for 39 and Inzamam (15) was caught off Jacques Kallis in the next over to kill off Pakistan's chances.
Abdul Razzaq (6) and Rana Naved-ul-Hasan (0) both fell in Kallis's next over as Pakistan slumped to a sorry 125 for eight.
Shoaib Malik and Mohammad Sami, who scored a career-best 46, batted courageously and their 73-run stand brought respectability to their total.
Shoaib top-scored for Pakistan with a defiant 52 not out, which included three fours and two sixes.
Earlier, Boucher launched nine fours and four sixes to propel South Africa to their huge score, taking advantage of the closing overs and lives on 24 and 48.
Openers Graeme Smith (72) and AB de Villiers (67) had set South Africa on their way with a first-wicket stand of 140. Captain Smith, playing his 100th ODI, scored his runs off just 47 deliveries, with 15 fours.
When seamer Naved-ul-Hasan returned for a second spell he hit him for 27 runs in an over which included six fours, two wides and a no-ball.
Kallis (88 not out) and Ashwell Prince (39) kept the scoreboard moving and Boucher and Kallis then added 128 for the fifth wicket off just 67 deliveries.
England's mark of 363 for seven against Pakistan, in 55 overs, in Nottingham in 1992, was Pakistan's previous most expensive one-day performance in the field.