Niasse has started just eight Premier League games this season, including each of the last three, but only Wayne Rooney (10) has scored more goals than his return of seven.
The 27-year-old found the net against Crystal Palace on Saturday in a crucial win over Crystal Palace, as well as setting up Gylfi Sigurdsson for the opening goal, and looks set to continue keeping Tosun and young talent Dominic Calvert-Lewin out of the team for the time being.
"His hold-up play and his work-rate were good," Allardyce said of Niasse (EvertonFC.com).
"He has got competition - obviously Cenk is very disappointed that he is not playing - but when somebody up front is doing the job as well as he can and making an impression on the team, then Dominic and Cenk have to be a little bit more patient.
"Oumar's goals-per-game ratio is good and he appears, at the moment, to be the best player to score goals for us. His contribution on Saturday helped us and, as a team, we now have to keep up that home form. The one thing we need to get better is the away results."
Having been knocked out of the FA Cup last month, the Toffees will not enjoy a break before resuming their Premier League campaign away at Watford on 24th February.
(You may also be interested in 'Sam Allardyce Explains the Thought Process Behind Deciding to Sign £27m Striker Cenk Tosun')