Farrell then had two opportunities to increase the Saracens' lead with penalty kicks, but the first drifted wide from distance while the second was dragged away from the posts.
Saracens put the visitors under pressure early in the second half and it paid off quickly, as Farrell brought his side to within a point with another penalty.
Tikoirotuma was sin-binned five minutes later and the reigning champions took advantage as Jackson Wray went over to put his side in front, but Farrell missed the conversion.
The hosts continued to press and the table-toppers finally established a strong lead as Alex Goode took it round a tackle to reach over the line, and Farrell this time nailed his kick to make it 18-7.
Two late Farrell penalties put the score beyond doubt as Saracens keep their 100% record while London Irish still search for their first point of the season, after Geraghty missed a penalty in the last minute that would have given them a losing point.