The former England skipper needed lengthy treatment from the club’s medical staff before he was allowed to rejoin the action.
Rooney protested heavily to referee Martin Atkinson over the challenge but the official refused to hand out any punishment to Francis.
The experienced forward suffered more problems just two minutes before half-time when his cut re-opened following a challenge with Adam Smith.
Rooney needed more treatment from the Everton medics after more blood was streaming down his face.
England’s all-time leading scorer eventually left the field on 55 minutes and manager Ronald Koeman is hopeful that he will be fit for their next game against Apollon Limassol in the Europa League on Thursday.