Hanzal caught Conacher in the face as the two crossed paths between the circles in the Phoenix zone. He went down to the ice and was bleeding immediately, but no penalty was called on the play. He was assisted off the ice and to the dressing room. However, he returned for the third period.
Conacher has one goal in Ottawa's first six games of the season.
The Coyotes played without defenseman Derek Morris, whose five points were tied for the team lead. He suffered a lower-body injury during Sunday's 5-3 road victory against the Carolina Hurricanes and was replaced in the lineup by David Schlemko.