The pair helped their side to 194 for three in the 33rd over but when they departed the innings folded, the last seven wickets falling for 83.
Paceman Rana Naved-ul-Hasan mopped up the tail to finish with four for 29.
"I thought we were very well placed, with Sarwan and Chanderpaul," said West Indies captain Brian Lara [ Images ]. "That's the point when the game started to change."
West Indies won the toss and made a reasonable start, reducing Pakistan to 90 for three in the 23rd over when the momentum suddenly changed as Youhana and Inzamam added 134 off 119 balls for the fourth wicket.
Inzamam smashed 10 fours before he was bowled by Dwayne Bravo [ Images ] with the total on 224.
Man of the match Youhana was more patient but no less effective. He managed nine boundaries but was more content to accumulate his runs through singles and twos.
He reached his 11th one-day international hundred off 95 deliveries but departed three balls from the end when he was caught short of his ground trying to scamper home for a second run.
Ian Bradshaw was the pick of the bowlers, capturing three wickets for 47 off 10 overs.
In reply West Indies lost Chris Gayle [ Images ] for a duck but still looked to be in with a chance of an unlikely victory when Sarwan and Chanderpaul added 95 for the fourth wicket.
Pakistan will now play Australia in the best-of-three finals series. The opening match will be played at Melbourne [ Images ] on Friday with the second match in Sydney [ Images ] on Sunday. A third match, if required, will be held in Adelaide next Tuesday.
Salman Butt [ Images ] c Browne b Bradshaw 19
Kamran Akmal c Bravo b Bradshaw 17
Yasir Hameed [ Images ] b King 24
Yousuf Youhana run out 105
Inzamam-ul-Haq b Bravo 74
Abdul Razzaq [ Images ] st Browne b Hinds 7
Shahid Afridi [ Images ] b Bradshaw 23
Shoaib Malik [ Images ] not out 8
Naved-ul-Hasan run out 3
Extras (lb-4 w-19 nb-4) 27
Total (for eight wickets, 50 overs) 307
Fall of wickets: 1-37 2-44 3-90 4-224 5-248 6-279 7-300 8-307
Did not bat: Iftikhar Anjum, Mohammad Khalil.
Bowling: Collins 10-0-46-0 (nb-4 w-1), Bradshaw 10-1-47-3 (w-5), King 10-0-60-1 (w-3) Hinds 5-0-44-1 (w-6), Bravo 10-0-55-1 (w-2), Gayle 5-0-51-0 (w-2)
C.Gayle c Kamran Akmal b Naved-ul-Hasan 0
R.Powell c Kamran Akmal b Naved-ul-Hasan 23
R.Sarwan st Kamran Akmal b Shahid Afridi 87
B.Lara c Iftikhar Anjum b Mohammad Khalil 19
S.Chanderpaul c Inzamam Iftikhar Anjum 58
D.Bravo b Shahid Afridi 1
W.Hinds c Inzamam-ul-Haq b Mohammad Khalil 30
C.Browne b Naved-ul-Hasan 36
I.Bradshaw b Naved-ul-Hasan 0
P.Collins c Mohammad Khalil b Iftikhar Anjum 1
R.King not out 3
Extras (lb-3 w-11 nb-5) 19
Total (all out, 48.1 overs) 277
Fall of wickets: 1-0 2-67 3-99 4-194 6-198 6-203 7-257 8-259 9-260
Bowling: Naved-ul-Hasan 9.1-0-29-4 (w-3), Iftikhar Anjum 9-0-67-2 (w-3), Mohammad Khalil 10-0-59-2 (nb-1 w-2), Abdul Razzaq 9-0-61-0 (nb-3 w-2), Shahid Afridi 10-0-47-2 (nb-1 w-1), Salman Butt 1-0-11-0
Result: Pakistan won by 30 runs
Man of the match: Yousuf Youhana (Pakistan).