Emmanuel Dennis fired Watford, who had their last two games postponed, into a fourth-minute lead with a fine left-foot effort from the edge of the box but Claudio Ranieri's side were unable to build on their advantage.
David Moyes' side thought they had a third through Bowen but VAR spotted a foul by Soucek on Dennis and the effort was over-turned.
Substitute Nikola Vlasic completed the rout, slotting home after good work from the impressive Bowen.
"I thought Jarrod played very well today, his assists were important and his link up play was as well today and a good combination with Vladimir [Coufal]," Moyes said.
"Him making the goals is a sign of his maturity and getting better with his last pass and decision."
West Ham end the year in contention for a European place for the second straight year after picking up 22 wins in 2021.
"We have had a great year, we really have. We have had a lot of wins this year. We are back challenging which was not the situation maybe even two years ago. To be talked about in the top four or Europe this year is a big turnaround," Moyes added.
The defeat leaves Watford hovering two points above the relegation zone in 17th place on 13 points.
"We score goals but it is important to maintain the clean sheet. We have to play better or help each other much better," Ranieri, whose team were hit hard by COVID in the past fortnight, said.
"The COVID situation is not an excuse but when you have had just one training session together it is not easy to prepare. I hope this week nothing happens and we can train every day," he added.