Morecambe finally clinched their first win of the season but Leigh pushed them all the way in this Bank Holiday encounter.
The Shrimps totally dominated the opening stages of the game but it was the visitors who ended the match on top with a determined late rally.
After two successive home defeats Morecambe were desperate for a victory and they started the game well with some neat football.
Wayne Curtis came close on two occasions and Michael Twiss forced Ian Martin into a superb save with a left-footed curler from the edge of the area which the keeper turned round the post at full stretch.
Martin could do nothing with Morecambe's opener on 32 minutes, however. Youngster Garry Hunter chose the perfect time to open his account for the first team with a stunning right-foot volley from 30 yards out that looped over the Leigh keeper's head.
Hunter then played a major role in Morecambe's second five minutes into the second half. After robbing Gareth Holmes of possession he threaded a ball through to Curtis, who drilled home his second goal of the season.
But as Morecambe fans celebrated Leigh hit back straight from the kick-off. Chris Simms found Alex Meechan and he produced an excellent finish.
After the goal Leigh found a new spark and Adam Sollitt had to do well to tip over a vicious Warren Peyton corner, before the visitors were denied an equaliser when Gareth Stoker's close-range volley came back off the crossbar with Sollitt beaten.
The Shrimps were then denied two penalties when Danny Carlton and Nick Rogan were bundled over in the box, but managed to hold on despite some intense late Leigh pressure.