Earlier on Saturday, 17th-placed Nottingham Forest were beaten 2-1 at home by Manchester City, to give the Hammers the chance to close the gap.
But the east Londoners, without a win since a 3-2 success over Burnley on 8 November, could not take advantage on another miserable day at London Stadium.
As well as the club struggling on the pitch, there have been frequent protests throughout the season from the Hammers fans, angry at the club’s direction under chairman David Sullivan and vice chair Baroness Brady.
In the 15th minute, to signify the 15 years they have been at the club, numerous fans held up red cards aimed at the pair, while chants of “sack the board” were also heard.
Part of the supporters’ anger is over the club’s business in the transfer market, and this performance again highlighted both West Ham’s lack of creativity and clinical finishing.
If the Hammers are to extend their 14-season spell in the top flight then Bowen, their top scorer with only five goals, will need to have a strong second half to the campaign.
He was at the heart of most of the hosts’ chances and had a first-time effort pushed over by Leno, while he twice looked to be through on goal, only to be denied by tight offside calls.
But Bowen would have been disappointed with his finish when Soungoutou Magassa had created the chance, only for the Hammers skipper to not get a clean contact and send the ball wide of the post.
Bowen was again involved as he released Wilson, but he shot over, with those missed opportunities proving crucial as Fulham left with the win.
“We have to demand more from ourselves, demand more from each other,” said Bowen. “The only thing I know is to stick at it and change your fortunes.
“It’s easy to blame, easy to point fingers and ultimately it comes from inside to put it right yourself starting from me first and foremost and that starts now.
“It’s a really good group and the main thing is we have to stick together as a team.”
The Hammers have now only picked up 10 points from Nuno’s 13 games in charge, with just Burnley and Wolves collecting fewer since he replaced the sacked Graham Potter at the end of September.