Alexis Sanchez put the hosts ahead when he nodded home Danny Welbeck's delightful dinked ball just before halftime but Bolasie equalised with a low drive from the edge of area that beat Petr Cech at his near post in the 82nd minute.
Arsenal dominated possession with Sanchez and Mesut Ozil close to scoring from free kicks, while the Germany midfielder was denied from point-blank range by visiting goalkeeper Wayne Hennessey just before the Chile forward opened the scoring.
Bolasie's leveller shook the fourth-placed home side and they were almost caught out again in stoppage time when only a last-ditch tackle from Gabriel Paulista stopped dangerous winger Wilfried Zaha in his tracks as he burst into the area.
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(Reporting by Alistair Smout; Editing by Ken Ferris)
