The 33-year-old Fleming, who overtook Sri Lankan Arjuna Ranatunga's captaincy tally of 193 matches, opened the batting and stood his ground till the 38th over to steady the faltering innings on Wednesday.
The Black Caps were reduced to 23-2 in their 500th One-dayer before being rescued by a fourth-wicket stand of 108 between Fleming and Styris.
Styris, who needed a runner in the latter part of his innings due to a back strain, smashed 10 boundaries to lead a late batting assault.
Jacob Oram slammed 31 off 26 balls as New Zealand plundered 99 runs in the last 10 overs in a match which will take the winners into the semi-finals from group B.
The other semi-finalist from the group, which also includes Sri Lanka and South Africa, will be determined after Friday's last league match between Pakistan and South Africa here.
New Zealand made a disastrous start on a seaming wicket as Umar Gul clean bowled Lou Vincent in the second over and new-ball partner Rana Naved had Nathan Astle (15) edging a catch to the slips in the eighth.
Peter Fulton helped Fleming take the score to 60-2 when he was trapped leg-before by Rao Iftikhar for seven in the 15th over.
Pakistan, who won the toss and elected to field, face a challenging target of 5.5 runs an over under lights to ensure their place in the semi-finals.
To lessen the dew that is expected to wet the ground in the second session - making it difficult for bowlers to grip the ball - organisers sprayed a chemical used in farming on the outfield before the start of the match.
"The chemical is not expected to eradicate dew completely, but it is hoped it will reduce it significantly," the International Cricket Council (ICC) said in a statement.
Last week, the ICC sprayed polyvinyl acetate, an adhesive commonly used for porous material, on the dusty wicket at the Brabourne Stadium in Mumbai in a bid to bind the surface for the entire 100 overs of the match.
Fall of wickets: 1-3 (Vincent), 2-23 (Astle), 3-60 (Fulton), 4-168 (Fleming), 5-220 (Oram), 6-254 (Styris), 7-270 (McCullum).
Umpires: Mark Benson (ENG) and Rudi Koertzen (RSA), TV umpire Billy Bowden (NZL)
Match Referee: Ranjan Madugalle (SRI)