Derek Adams made two changes to the Morecambe side that drew against Shrewsbury Town with Jensen Weir and Jake Taylor handed their debuts in midfield.
With just nine minutes on the clock, Ward tried his luck with an effort from 25 yards which went straight through Connor Ripley’s hands and ended up in the back of the Morecambe net.
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Ward went close again before the Shrimps should have levelled as Stockton was played through but, with only Lucas Bergstrom to beat, shot straight at the keeper.
Ripley made amends for his earlier error with fine saves from Thompson and Jack Marriott but the home side added a second two minutes before the break.
Ripley did well to turn away Jonson Clarke-Harris’ fiercely-struck free-kick but the Shrimps failed to clear their lines and Thompson volleyed home the loose ball from the edge of the area.
The second half started with Peterborough thinking they had won a penalty when Ripley clipped Clarke-Harris in the area – but the assistant referee wrongly flagged for offside.
The decision seemed to give the home side a spark as they took charge again.
Ripley saved smartly from Marriott’s close-range shot on the turn before Grant McCann’s team added a third on 72 minutes.
Ash Hunter was dispossessed on the edge of the Peterborough box and the home side countered quickly, Marriott teeing up Kyprianou who slotted the ball under Ripley.
The Shrimps had another great chance for a consolation on 88 minutes, only for substitute Jon Obika to volley over from Shane McLoughlin’s pinpoint cross.
Peterborough United: Bergstrom, Edwards, Knight (Ajiboye 74), Kent, Jack Taylor, Kyprianou, Ward (Thompson 80), Burrows (Tomlinson 80), Thompson (Randall 74), Clarke-Harris, Marriott (Joe Taylor 74). Subs not used: Lakin, Fuchs.
Morecambe: Ripley, Rawson, Delaney, Gibson, Love, Melbourne (Watts 69), Taylor (McLoughlin 74), Weir, Fane, Hunter (Connolly 74), Stockton (Obika 74). Subs not used: Smith, Gnahoua, O’Connor.
Referee: Dean Whitestone