It was a dream start for Prica as the hosts ran out 2-0 winners against relegation rivals Birmingham City at the Stadium of Light.
Daryl Murphy got the Wearsiders off to a great start when he caught City napping and reacted quickest to fire the Black Cats in front on 15 minutes.
A long free-kick from just inside the Birmingham half was hoisted forward by former Manchester United man Phil Bardsley, also making his Sunderland debut.
Kenwyne Jones got up to head the ball on and with the visitors defence rooted to the spot Murphy netted with a powerful close-range effort.
In truth it was no more than the home side deserved as they took the game to the Blues from the off.
Both teams looked to attack when possible but despite the play being fairly open out and out chances in front of goal were limited.
Jones and Murphy both went close for the hosts without really troubling goalkeeper Maik Taylor, while Blues striker Cameron Jerome should have caused problems for Black Cats keeper Craig Gordon.
With the half drawing to a close, City hit Sunderland on the break and Jerome bore down on goal with number of home defenders in close pursuit.
However, the one-time Sunderland target found £9million man Gordon more than a match for his effort, the former Hearts player parrying his shot out for a corner.
The Blues started the brighter after the break, Olivier Kapo firing narrowly wide from 20 yards out on 47 minutes.
The Black Cats came back into the game after that scare, but the defence was wide open again on 64 minutes when Jerome almost pulled a goal back.
Hesitation in the Sunderland defence saw Nyron Nosworthy sell Gordon short with a header. Jerome tried to reach the ball, but Gordon bravely punched clear and instead the former Cardiff City forward made contact with the keeper, conceding a free-kick in the process.
Four minutes later Prica got his Sunderland career off to a flying start. Liam MIller lofted the ball towards the 18-yard box and Birmingham defender Liam Ridgewell stooped to head back to Taylor.
Unfortunately for the Blues the header fell short and Prica nipped in to put the ball past Taylor and into the net.
The Swede could have made it a double delight eight minutes later when a ball over the top dropped invitingly in the six-yard box.
The forward fell as he tried to connect, but still managed to swing out a leg while on the floor and knock the ball home. Sadly for the frontman the ball had hit his arm as he dropped to the ground and referee Mark Halsey blew for handball.
The debutant went close again in the dying minutes, cutting in behind the City defence to head for goal. However Taylor made a good save to deny him further glory.
Sunderland finished with a flourish without adding to their two-goal tally, but that won't worry them too much now that they have moved out of the relegation zone.