Both sides showed plenty of changes following midweek games with Wrexham's six new faces including a debut for defender Joe Worrall.
The hosts enjoyed the majority of the possession in the opening stages in which Castellanos headed over from Solomon's cross.
A determined run from the outstanding Bowen into the area then saw him unleash a shot which Anthony Patterson managed to divert on to the post.
From the resulting corner Mavropanos' header was wide of the target with Max Kilman failing to apply a final touch at the far post.
Piroe fired over before West Ham's pressure finally told and it was their talisman Bowen with his sixth goal of the season.
On-loan Divine Mukasa and Solomon combined to set up Morato, whose low cross was met by Bowen to net from close range.
With West Ham firmly in control, Wrexham were pinned back in their own half for most of the opening period and restricted to rare counter attacks.
Danny Imray saw a shot blocked while George Dobson - facing his boyhood club - saw his shot cleared off the line by Mavropanos, who had initially lost possession.
No sooner had Wrexham missed the chance to level that West Ham went further ahead as Castellanos beat the offside trap to set up Piroe to fire home.
The hosts kicked off the second half in the same vein as Bowen's long pass found Solomon who was denied by Patterson before Mavropanos extended their lead a minute later from Bowen's corner.
West Ham were impressive on the counter-attack from one such move Bowen fired wide before substitute Kyle Walker-Peters' fine run set up Castellanos to slot home the home side's fourth.
Kante received the ball over the top from Solomon to make it 5-0 with 14 minutes remaining.
Solomon then capped a man-of-the-match performance and was rewarded with the final goal when his left-footed shot beat the goalkeeper off the post.
It was a sensational display from the Hammers and a warning to their Championship rivals.
Wrexham, who had only conceded five goals in their previous six games, will need to regroup before next Saturday's game against Southampton.
Image source, Rex Features
