The wicket-keeper's exit for 82, however, sparked a mini-collapse that saw three wickets lost for six runs.
Victory left England 2-0 up in a three-match series that concludes at the Ageas Bowl, the venue for all three matches, on Tuesday.
Left-arm paceman Willey, who took an ODI-best 5-30 last time out, dismissed Gareth Delany and Paul Stirling after Ireland captain Andy Balbirnie, somewhat surprisingly, decided to bat first.
Campher came into bat with Ireland again deep in trouble at 78-5.
This series, being played behind closed doors because of the coronavirus, also launches the new World Cup Super League, which will determine qualification for the 2023 50-over showpiece in India.