The strikers, two of 11 summer recruits at Victoria Park, ensured Ronnie Moore’s men followed last term’s great escape with a winning start to the 2015-16 season.
The hosts, featuring six new faces in their XI, began impressively – although they almost fell behind when Ryan Edwards headed against the crossbar.
Pools were undeterred and took a 25th-minute lead through one of their new signings.
After Michael Woods had seen a powerful effort saved by Barry Roche, Bingham collected the ball and sent in a perfect centre for skipper Paynter to head his 100th league goal into the corner.
Jamie Devitt and Lee Molyneux spurned glorious chances to level either side of half-time, with the Shrimps growing into the contest.
However, that good spell came to an end as Hartlepool doubled their advantage.
Paynter was the orchestrator, cleverly finding space before chipping a delicious through-ball to Bingham – who powered home emphatically.
Morecambe still looked dangerous, which was shown when veteran winger Kevin Ellison rattled the woodwork, yet Pools held on to claim the points.