The visitors had a chance to open the scoring earlier in the game when they were awarded a penalty, only to see Svetoslav Dyakov miss after tamely firing at Berisha.
The home side had a penalty of their own in the second period when Felipe Anderson was brought down inside the box after wriggling away from his marker.
The Brazilian picked himself to take the spot kick but saw his effort saved by Vladislav Stoyanov five minutes after the restart.
Ludogorets were then reduced to 10 men when Dyakov picked up his second yellow card for a foul on Lucas Biglia, but Lazio's numerical advantage was wiped out on 73 minutes when Luis Pedro Cavanda was given his marching orders for a high tackle.
The Bulgarian side held on for the win as loud boos echoed around the Stadio Olimpico after the final whistle.