Owen, who is now with Worcester Warriors, started his first match of the tournament having been a replacement in the defeat by Ireland in the opening round of matches.
Having lost to Ireland England got back to winning ways, but crucially missed out on a four-try bonus point against Italy in Santa Fe
England held a narrow one-point lead at the break through an Alex Coles converted try while Italy sent over two penalties via Giacomo Da Re.
Steve Bates’ side scored second half converted tries through Tom Willis and Richard Capstick, with Italy responding via Cristian Lai, Ange Capuozzo and Paolo Garbisi but Josh Hodge’s late penalty won the game.
England will next face pool leaders Australia, who have maximum points from their opening two games with victories over Italy and Ireland, on Wednesday.
“It was a tough game, Italy played well but we put them under a lot of pressure but didn’t turn that pressure into points and they capitalised on the opportunities they had,” said England Head Coach Bates.
“We will look back and say we made far too many individual mistakes, but credit to our guys for fighting back in the manner they did to get the victory and the guys should be proud of that.
“The standard of rugby in this tournament is increasing each year and with every game and we’ve had two physically demanding games which the players have put everything into so the challenge will be for the players to recover and pick themselves up for the final pool match against Australia.
“It’s disappointing the position we’re in as we’ve come here to win the tournament but if you don’t play well then you are going to struggle as there are no easy games in this Championship.
“We will go into the Australia game looking to give a good account of ourselves and whatever happens after that we will deal with.”