Rajiv van La Parra curled home a stunning first-half strike just before the interval and the Terriers then held on after defender Christopher Schindler had been sent off early in the second period.
"I know that when we played Man United this was a big win," said Wagner, whose players ran themselves to a standstill following Schindler's 57th-minute dismissal for two yellow-card offences.
Huddersfield Town ratings: Who stood out in West Brom win
"I think it was a big win for the football club, while today it was a big win for us as a group and for me as a manager.
"We've shown we can play in our identity and style and also, if we need to, we can play in the deeper block if necessary and I'm absolutely delighted the players have shown both."
Wagner acknowledged Van La Parra's brilliant goal and the huge role played by goalkeeper Jonas Lossl, who denied West Brom substitutes James McClean and Matt Phillips in stoppage time with full-length diving saves.
"He (Lossl) was there when we needed him," Wagner said. "For 85 minutes he didn't have anything to save, but then he was there with two world-class saves and this is high quality.
"It was his fifth clean sheet and an important one because if you have a clean sheet and score once you have three massive points."
Wagner felt Schindler's first booking after his challenge on West Brom striker Hal Robson-Kanu was harsh, but did not want his dismissal to overshadow his side's performance.
"It was a deserved win because the players have shown, for the first 60 minutes, high intensity, energetic football and for the last 30 minutes the spirit and fighting attitude that you need to be successful."