Stephen Moore (44) and Phil Jaques (95) put on 97 for the first wicket but once Salisbiry trapped the former, Worcestershire lost wickets at regular intervals and Daryl Mitchell was the lone face of defiance with an unbeaten 54.
Kumble got a vital breakthrough when he caught rival skipper Vikram Solanki (17) off his own bowling and then Salisbury grabbed two more -- Ben Smith and then Jacques -- and Worcestershire found itself in the rut.
Anil Kumble returned Stephen Davies and then claimed the last three wickets, including that of former Team India colleague Zaheer Khan (4), who was trapped leg before.
Kumble's figures read 33-8-80-5.
Surrey reached 42 for no loss in reply before the close of play.
Zaheer Khan bowled seven fruitless over, including a maiden, which cost him 22 runs