Tsotsobe had proved his fitness over the first two rounds of Sunfoil Series games, and on Sunday he showed form in taking 5 for 44 to bowl the Warriors out for 271 at Senwes Park.
A 115-run stand for the second wicket between Jon-Jon Smuts and Colin Ingram had the Warriors on track in their chase of 292, taking them to 159 for one in the 32nd over.
However, Kagiso Rabada struck the crucial blow, bowling Ingram off the inside edge for 65, before Tsotsobe got rid of Ryan Bailey.
After Hardus Viljoen had caught and bowled Smuts for 89 and then trapped Somila Seyibokwe lbw, Tsotsobe picked up the wickets of Christiaan Jonker and Andrew Birch in the same over and then completed his five-wicket haul in his final over.
That left the remaining Warriors batsmen with too much to do, as they were bowled out with three balls left unused.
The Lions innings had been steady throughout thanks to three half-centuries.
Quinton de Kock provided the early momentum with his 56 and, once he was gone, Neil McKenzie stroked his way to 73 whilst keeping the run-rate above five per over.
Thami Tsolekile then added the late runs as he smashed 51 not out from just 36 balls to see the Lions to a score of 291 for five.
Tsotsobe was named man of the match as the Lions matched the number of one-day games that they won last season in their first outing.