Bouanga ripped a right-footer from the left corner of the penalty area into the back of the net to cap the scoring in the fifth minute of stoppage time.
New York (4-1-4) is unbeaten in five straight games since a 3-0 loss to the Columbus Crew on March 16.
LAFC’s Aaron Long blocked a shot from Dante Vanzier in front of an open goal but slid into the post and was forced to come off in the eighth minute. Eddie Segura came on and — on the corner kick conceded by Long’s block — surrendered an own goal on his first touch to give New York a 1-0 lead.
Bouanga was fouled in the area by Sean Nealis and converted from the penalty spot to make it 1-1 in the 67th minute.
Emil Forsberg scored on a half-volley to give the Red Bulls a 2-1 lead in the 81st. John Tolkien played a corner kick that was redirected and dropped in front of Forsberg for the finish from point-blank range.
LAFC (3-3-3) had 57% possession and outshot New York 15-7.
Carlos Coronel had four saves for the Red Bulls. Hugo Lloris had one save for LAFC.