New Zealand got off to a poor start when Craig Cumming (3) was caught by Yasir Hameed, who juggled the ball before holding on to it, off the bowling of Mohammad Sami with the score on 10.
But New Zealand quickly increased their run rate as Marshall raised his half-century in 57 balls with four boundaries, while opener Fleming was even more ruthless with the Pakistan bowlers and raced to his half century in 48 balls, stroking eight fours.
Following the departure of Marshall, who was caught by Sami off Shoaib Malik in the 30th over, Scott Styris (20) and Craig McMillan (36 not out) supported their skipper to guide New Zealand home with 3.4 overs to spare.
He wasted little time adding to that total when he snared the impressive Elahi at mid-wicket.
Pakistan
Y Hameed c Styris b Oram 44
I Farhat c McCullum b Mills 17
S Elahi c Fleming b Styris 80
Y Youhana run out 36
Inzamam-ul-Haq c McCullum b Tuffey 0
Shoaib Malik c Fleming b Tuffey 0
M Khan c Mills by Styris 10
A Razzaq not out 50
A Mahmood run out 11
S Akhtar run out 2
M Sami not out 0
Extras (lb2, w2, nb1) 5
Total (nine wickets, 50 overs) 255
Fall of wickets 1-50, 2-72, 3-144, 4-144, 5-152, 6-186, 7-190, 8-234, 9-247
Bowling: Tuffey 10-2-45-2, Mills 10-0-58-1, Oram 10-0-48-1, Cairns 9-0-54-0, Vettori 8-0-34-0, Styris 3-0-14-2.
New Zealand
C Cumming c Hameed b Sami 3
S Fleming not out 115
H Marshall c Sami b Malik 64
S Styris b Akhtar 20
C McMillan not out 35
Extras (lb-14, w-5, nb-3) 22
Total (for 3 wkts, 46.2 overs) 259
Fall of wickets: 1-10, 2-158, 3-188
Bowling: Akhtar 10-0-43-1, Sami 10-0-67-1, Mahmood 10-0-43-0, Razzaq 8-0-47-0, Malik 8-0-40-1, Farhat 0.2-0-5-0.