The Hammers had lost the top spot to West Brom on Wednesday after the Baggies claimed a narrow 1-0 win at Derby, thanks to Aune Heggebo and despite playing for more than an hour with 10 men following Brayann Pereira's dismissal.
Bowen opened the scoring on 28 minutes when he touched home Morato's low cross for his sixth goal of the season.
Argentina international Taty Castellanos selflessly teed up Dutch-born Suriname forward Joel Piroe to double West Ham's lead on 37 minutes.
And the contest was all but over three minutes after the restart as Greece centre-back Konstantinos Mavropanos headed home Bowen's corner.
Castellanos was next to get in on the act as he scored from a pass by Kyle Walker-Peters.
Manor Solomon played in substitute Mohamadou Kante for the fifth and scored the sixth himself from Walker-Peters's square pass.
West Brom could regain top spot with victory at home to fourth-placed QPR on Saturday.
QPR, Charlton and Swansea could all mathematically overtake West Ham, but they would need to win by unlikely scorelines to do so.