The England Under-21 international flung himself to block a close-range shot after Gornell had been set up by a precise ball across the box from Steve Jennings.
Earlier, as Tranmere posed the biggest first-half threat pumping long balls forward, Lewis saved well from Ian Moore and then Gareth Edds and Moore, son of Rovers boss Ronnie Moore, had close-range efforts blocked in quick succession.
George Boyd, playing in a midfield role, split Rovers with a superb cross field pass only for Russell Martin to deliver a poor cross and it was the 25th minute before Danny Coyne was forced into action for the first time, going full-length to his right to hold an awkwardly bobbling 30-yard drive by Aaron McLean.
Top Posh marksman Craig Mackail-Smith worked hard yet was well wide with a header and failed to get any force behind a shot when Charlie Lee's off-target shot came his way.
Shaun Batt, who rescued Posh with a last-ditch equaliser at Swindon in midweek, replaced Lee at the break and announced his arrival with a surging break on the right, before turning inside to send a right-footed shot wide of the far post.
Although Posh were more adventurous in the second period, Tranmere dropped back in numbers with Ian Goodison and Ben Chorley solid in front of the agile Coyne.
The Tranmere cause was also helped by wayward finishing as both Batt and McLean fired well wide.
Tranmere's Bas Savage failed to do any better in a rare opening at the other end with a mis-hit shot which barely rolled into Lewis' hands.