The Toffees, who had won two of their previous three outings, took the lead in the 58th minute when Leighton Baines curled home from the edge of the penalty area after Seamus Coleman had been tripped.
Four minutes later Saha, back after four months on the sidelines, doubled his side's lead with a low effort from 20 yards.
Birmingham, the Carling Cup holders, reduced the arrears after 79 minutes when Adam Rooney converted a cross from Morgaro Gomis.
Source: Team Talk
Source: Team Talk