The 34-year-old left-hander notched an unbeaten 107 -- his ninth one-day hundred -- but failed to get much support at the other end as Pakistani bowlers kept it tight to dismiss the West Indies for 208 in the 49th over.
Pakistan were also restricted by some disciplined deliveries by Jerome Taylor (3-38) and Daren Powell 3-50, with the team eventually bowled out for 232 in 49 overs on a slow Sheikh Zayed Stadium pitch.
The third and final match is on Sunday.
Chanderpaul, who took 12 deliveries for his first run, hit six boundaries during his 149-ball knock but failed to keep the asking rate in control.
Pakistan needed early wickets and Tanveer provided them with Chris Gayle (nought) and Sewnarine Chattergoon (nought) in his first spell, putting the West Indies on the back foot.
Chanderpaul, declared player of 2007 for his prolific scoring, added 92 for the third wicket with Ramnaresh Sarwan (45) as the two steadied the innings.
But leg-spinner Shahid Afridi broke the stubborn stand when he trapped Sarwan leg-before with a faster delivery, leaving the fight to Chanderpaul.
Chanderpaul, dropped on 17 and 63 -- both times by Saeed Ajmal, kept one end intact but Umer Gul (3-44) and Tanveer (2-32) wrapped up the innings.
Pakistan captain Shoaib Malik said Gayle's wicket was pivotal.
"We didn't have a big total to defend so we knew Gayle's wicket was crucial," said Malik of his counterpart who was bowled off a swinging yorker by man-of-the-match Tanveer.
Earlier Pakistan were rescued by Misbahul Haq (52) and Younus Khan (34) who put on 51 runs for the third wicket after Pakistan lost both the openers for just seven.
Younus hit five boundaries while Haq managed just one during his slow 86-ball knock.
Pakistan were further jolted when Malik was run out for 10.
It was left to Akmal, who hit Taylor for two sixes in the 50th over to give Pakistan an unexpected win in the first match on Wednesday, and Shahid Afridi (28) to give some respectability to the innings.
Akmal scored 45 off 54 balls with just one boundary.
He shared a rapid 52-run stand for the sixth wicket with Afridi before West Indies hit back, dismissing both in the space of just two runs.
Tanveer (26) used the long handle effectively, hitting Taylor for three boundaries in the 48th over before he was run out.
West Indian coach John Dyson said early wickets was a setback.
"I think losing both the openers was crucial and Tanveer swung the ball nicely," said Dyson, a former Australian opener.
Pakistan had to leave out paceman Shoaib Akhtar for the second match in row after the flamboyant bowler failed to fully recover from a calf muscle injury.
Pakistan brought in fast bowler Rao Iftikhar and off-spinner Ajmal, dropping Abdur Rauf and Fawad Alam from the first match line-up.
West Indies replaced Brendan Nash with Shawn Findlay.