Seamer Hasan Ali became the quickest bowler to reach 50 ODI wickets for Pakistan as his 5-34 saw Sri Lanka bowled out for 208 in 48.2 overs at Sheikh Zayed Stadium in Abu Dhabi.
Imam, whose uncle Inzamam is now a Pakistan selector, became only the second batsman from his country and 13th overall to score a hundred on ODI debut before he finally fell for 100 off 125 balls.
The 21-year-old hit two sixes and five fours as the nominal hosts wrapped up the series with two matches to spare.
But Imam could have missed that milestone as he was reprieved on 89, having been given out caught behind by Niroshan Dickwella off Lahiru Gamage.
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As he was walking back, television umpire Richard Kettleborough found the ball had touched the ground before reaching wicketkeeper Dickwella's gloves.
A relieved Imam returned to the crease and completed his hundred.
Mohammad Hafeez remained not out on 34, scoring the winning single.
Imam said his heart was in his mouth when he was given out.
"But Hafeez told me to wait as the ball had touched the ground, so I am lucky and proud to have scored a hundred on my debut and that too with a record."
Pakistan hold an unassailable 3-0 lead in the five-match series after winning the first match by 83 runs in Dubai and a 32-run victory in the second in Abu Dhabi on Monday.
The remaining games are in Sharjah on Friday and Monday.
Zaman fell for 29, stumped by Dickwella off spinner Jeffrey Vandersay while Babar Zaman was bowled by Gamage for 30.
Sri Lanka, who suffered their ninth straight ODI defeat, were loose with the bat.
Hasan, 23, was ably assisted by leg-spinner Shadab Khan (2-37) as Sri Lanka, who won the toss and batted, lost their last nine wickets for only 106 runs.
Sri Lanka skipper Upul Tharanga (61) and Dickwella (18) put on 59 for the first wicket, but from 102-1 in the 26th over their innings was derailed by Pakistan's bowlers.
Tharanga, who hit a brilliant 112 not out in the previous match, hit five boundaries during his 80-ball knock.
Hasan, who had given Pakistan the early breakthrough with Dickwella's wicket, removed Chamara Kapugedera (18), Milinda Siriwardana (two) and Vandersay (nought) to complete 50 wickets in his 24th ODI.
The previous record was held by legendary paceman Waqar Younis, who took 27 ODIs to reach the mark. Sri Lankan spinner Ajantha Mendis holds the overall record of 19 matches.
Lahiru Thirimanne (28) and Thisara Perera (38) took Sri Lanka past the 200 mark.
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