Barry was named Albion captain at the Emirates Stadium in honour of his milestone moment and received a warm reception from both Arsenal and West Brom fans before kick-off.
The 36-year-old, who drew level with former Manchester United star Giggs when he played in West Brom's goalless draw against West Ham last weekend, was making his 601st start in the top-flight.
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Barry made his debut for Aston Villa at the age of 17, appearing as a substitute in a 3-1 victory at Sheffield Wednesday on May 2, 1998.
It was fitting that his landmark appearance came against the Gunners as their manager Arsene Wenger twice tried to sign him during his long career.
Instead, Barry went on to play for Manchester City, with whom he won the title in 2012, and Everton before joining West Brom on a free transfer this summer.
Now in his 21st season as a professional, Barry, who also has 53 England caps, this week admitted he could carry on playing until he is 40.
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That could take him past Giggs again as the Welshman, who played 40 times in the old First Division before the Premier League was introduced in 1992, made 672 top-flight appearances.
England manager Gareth Southgate played alongside Barry at Villa and he led the tributes to his former team-mate.
"It's been a great honour to watch you both winning titles with your club, and go on to over 50 caps with England, playing in the biggest of games," said Southgate of Barry. "I think back to watching for the first time as a young kid at Villa and realising straight away that I was in trouble for my place. Thankfully we played three at the back and you were able to play alongside me.”
He added: "I wanted to congratulate you on a fantastic achievement. You've become a role model on being able to keep playing for so long at such a high level. You're now in the history books and deservedly so. You've been undervalued by many for the way that you've played. Congratulations, enjoy it, and I dare say there's a few more games in the bag yet."
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