Bowen's double noticed the Hammers cross factors clear of London competitors Arsenal as David Moyes's guys published their third straight league win.
By assessment, this was Norwich's 6th successive defeat with out scoring and the Canaries are nevertheless three factors shy of protection, although a Watford side soaring above the relegation quarter have games in hand.
Former Hull winger Bowen's 7th and 8th dreams of the season will bolster the growing clamour for him to get an England call-up.
In a fit re-arranged from December because of a Covid-19 outbreak in the Canaries' camp, Tomas Soucek was lacking for the Hammers but complete-back Aaron Cresswell back after six weeks out with a back damage.
Milot Rashica saved his region for Norwich after scoring the winner of their FA Cup tie in opposition to Charlton.
Bowen nearly placed West Ham ahead inside two mins at the London Stadium whilst he was located via Manuel Lanzini's ball into the box, but his shot became too near Norwich goalkeeper Tim Krul.
Lanzini went close moments later and Krul became lucky to avoid conceding a penalty whilst he clashed with Nikola Vlasic on the intention-line, shoving the ahead to the turf via his face.
West Ham had the ball in the net within the 35th minute whilst Bowen's go went directly in but that attempt became disallowed given Vlasic was offside.
Their dominance, however, became rewarded 3 mins earlier than the ruin while Bowen were given ahead of Ben Gibson to move in a pass from Vladimir Coufal.
