The Baggies headed to St Mary's with just three wins in 14 league games but returned to form in style, with Marc-Antoine Fortune, Romelu Lukaku and Shane Long all scoring in a 3-0 win.
The three points saw them set a new club record for Premier League points (48) and wins (14), although it is referee Robert Madley's top-flight debut that stole the show.
The Yorkshireman sent off Saints pair Gaston Ramirez and Danny Fox as well as West Brom's Fortune - something manager Clarke hopes does not draw attention away from his side's fine performance.
"I think the win is the most important topic," he said. "We've been scratching around for a win a bit recently. The performances have been okay by and large. We have become a little bit of a reactive team, where we wait to the game happens and then we go chasing it.
"We do that quite well but we spoke about getting the first goal, we did that and from there we controlled the game. It was almost a perfect away performance.
"The three front players were great, not just causing Southampton a problem but defensively they worked hard for the team, closed the game down at the right times.
"The shape of the team was good - something we've worked on this week. It is nice when it pays off."
Clarke had not seen a replay of Fortune's sending-off before speaking to the media but agreed with Madley's decision to send off Ramirez and Fox.
"They tell me Marc pushed him and his hand caught him in the face so if that is the case we will take the punishment," he said. "I thought the other two red cards were clear as well, although it is a shame when a game finishes 10 against nine."