The England attacker, who is on loan from Manchester United, scored and provided an assist in the first half as his team raced to a 3-0 lead.
West Ham were, however, pegged back by Arsenal and ended up drawing the Premier League contest at home 3-3.
The result means they are still fifth in the Premier League, but could not significantly close the gap to the top four teams.
Lingard posted on Instagram post-game, saying: "Disappointed not to take the 3 points, alot to take away from the game.
"This team have come along way and I'm proud to be apart of it.
"Onwards and upwards #coyi #JL11NGZ"