The result left Red Star second on 44 points from 21 matches, six behind Partizan who visit seventh-placed Sloboda Uzice on Thursday.
Having given their new coach Ricardo Sa Pinto a winning start with a 2-0 home defeat of Radnicki Kragujevac on Saturday, Red Star produced another good performance as they seek to stop Partizan from clinching a record sixth successive league title.
The 25-year old Dauda, who joined Red Star from Swedish side Kalmar during the mid-season winter break, headed the hosts into an early lead after a teasing Nenad Milijas corner.
He doubled his tally shortly after the break with a superb back-heel from the edge of the five-yard box and then put through strike partner Darko Lazovic to make it 3-0 on the hour.
Dauda, who also rattled the crossbar with a curling shot from 20 metres as Red Star pressed forward, paid tribute to the club's passionate fans after the final whistle.
"I enjoy playing in this fantastic atmosphere and it lifted us after a slow start," he told Serbia's Arenasport television.
"We upped the pace after the first goal and all the credit for the second goes to (left back) Filip Mladenovic, who found space on the flank and whipped in a perfect cross."
Red Star's next game is away to bottom team Smederevo, who are 10 points adrift of safety and staring at relegation after managing only one win and six draws in 21 games.