Rizwan and Irfan both suffered hamstring injuries in the third match in Rawalpindi, where a second-string New Zealand side won by seven wickets to level the five-match series 1-1
The tourists resumed their second innings on 65 for two on a wicket that provided plenty of assistance for the seam bowlers and when dangerous opener Kusal Perera was out for 64, their hopes of saving the test were realistically over.
Sri Lanka had suffered crippling injuries to their bowling attack in the Test and were also without middle-order batsman Dhananjaya de Silva for the second innings, a major concern for their home series against England that starts on Jan 14.
The tourists posted an impressive 396 in their first innings, but allowed South Africa to amass 621 in reply, and will need to find more potency with the ball ahead of the second Test that starts in Johannesburg on Jan 3.