The attacker got the only goal of the game in a 1-0 win at St. Mary’s Stadium on Boxing Day.
The result moves West Ham further clear of the relegation picture, going four games unbeaten in the top flight.
Post-game, Bowen said: “A lot of things happened early in the game, but we knew it was going to be tough coming here, with them having a new manager.
“We had the same situation at Leicester, where we probably didn’t cope with it well enough, but we knew they’d have a lot of energy and probably have lots of chances, so it was about being able to control that.
“I think we had a few chances in the first half, and then they got a foothold in the game. But in the end it takes everything to win games in the Premier League, and if you’re one per cent down you get punished. The goal we got was a moment we took, and it’s meant we’ve won all three points.
“We needed to win this game. We knew that, coming off the back of two decent results, which were good draws, but we want to win games. Coming here today, we knew we had to win, and thankfully we’ve managed to do that.
“There are a lot of games in December and we knew it was a good opportunity to get points on the board, and we’ve done that with eight from the last 12. We know it could have been more, having conceded late on at Bournemouth, but overall it’s been a good run and we’ve gained a lot of confidence.”