Rodwell, who arrived on Wearside in a reported £10million deal from Manchester City earlier this week, played the opening 45 minutes at Bishop Auckland’s Heritage Park ground.
There was also a place in the starting XI for Santiago Vergini, who has returned to the Stadium of Light on a season-long loan deal having spent five months with the Black Cats last term.
One moment of concern for Poyet came in the first half when Emmanuele Giaccherini limped out of the action and down the tunnel with Jordi Gomez sent on in his place.
Scottish striker Steven Fletcher was sent on for Adam Johnson midway through the second period and he broke the deadlock with 11 minutes remaining after being gifted possession by the Real Betis defence.
And fellow frontman Connor Wickham, one of a few players to feature for the full 90 minutes made it 2-0 with time running out as he hammered home from long range.