The winger had a hand in each of the visiting side's goals, crossing for Alou Diarra and James Tomkins to head in before Ravel Morrison converted a spot-kick won by the 27-year-old
Sam Allardyce's side were beaten 4-1 by Mainz on Saturday but bounced back at the Flensburger Stadion thanks to goals from Alou Diarra, James Tomkins and Ravel Morrison.
The Premier League side made the better start and were rewarded after 15 minutes when Diarra headed home following a Matt Jarvis cross.
And just 13 minutes later, Tomkins doubled his side's lead with a similar goal. Man of the match Jarvis delivered a perfect cross again, and this time it was the turn of the centre-back to nod in.
West Ham were in cruise control but, after 42 minutes, Heiko Westermann scored the game's third header to reduce the deficit.
However, Morrison struck from the penalty spot on the stroke of half-time after Jarvis had been fouled in the box to send the Londoners in 3-1 up at the break.
Chances were at a premium in a second half that saw a number of changes, with the only scare for Allardyce and his team coming when Kevin Nolan went down with a knock.
The midfielder was fit enough to continue, though, as West Ham saw out the match comfortably. They now take on Eintracht Braunschweig in the final game of their tour on Saturday.