Tomorrow's match at Old Trafford is England's first ODI since their Champions Trophy semi-final defeat by eventual tournament winners Pakistan in Cardiff in June.
That match saw regular ODI opener Jason Roy dropped after a run of low scores, with Bairstow making 43 after being brought in at the top of the order.
Surrey batsman Roy was out for a golden duck in Saturday's lone Twenty20 international against West Indies at Chester-le-Street and Morgan confirmed Test wicket-keeper Bairstow would open on Tuesday.
"We feel Jonny deserves a chance. He's been waiting in the wings for quite a while now.
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"This is an opportunity to make the opening position his."
Bairstow's innings was one of the few crumbs of comfort England could take from a convincing eight-wicket defeat by Pakistan at Cardiff's Sophia Gardens.
England won 3-0 in a limited overs series in the Caribbean in March and were 2-1 victors on home soil in a recent Test campaign against West Indies.
But neither of those contests featured the likes of star batsmen Chris Gayle and Marlon Samuels, now back in the fold after a bitter dispute with Cricket West Indies officials.
"A lot of our focus over the last couple of years has been on ourselves.
"I think to make that extra step, learning on from the Champions Trophy, this series for us is about producing consistent performances.
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