Cris Carter held the previous mark of 58. Wayne now has made at least three catches in 59 consecutive games.
"Right now, it doesn't even matter," Wayne said. "Like I've been saying from Day 1, I see the light. I'm trying my best just to win games. That's what I want to do.
"When you win games, everything else will take its course. At the same time, whenever you play 12 years, you're bound to do something. There's something coming. I'm just happy to be still playing."
The Pro Bowl receiver also passed former Redskins receiver Art Monk for 12th on the NFL's all-time receptions list during the first half. Monk finished his career with 940 catches. Wayne now has 943, and he played a key role in a late first-half drive that ended with a 19-yard field goal from Adam Vinatieri as time expired.
"That's what is hard to do in this league," Wayne added. "Everybody's good. Whenever you can go out and keep being consistent, that's big. That's the same motto I've been having my whole career. I want to be able to be available whenever my number's called."
The Associated Press contributed to this report.