Linfield settled early and Fitzpatrick tested Marty Gallagher with a low angled shot inside the opening few minutes, but the Limavady United keeper got down well at his near post to deflect the ball away for a corner.
Gallagher was called into action again moments later, this time denying Frizzell, as Linfield continued to dominate the opening exchanges.
The home side seemed content to sit deep and hit on the break and the tactic almost paid dividends just before the half hour when Alfie Gaston flashed a low right foot shot inches past the post.
But the goal the visitors had been threatening arrived six minutes before half-time thanks to last season's leading goalscorer Fitzpatrick.
The big striker timed his run to perfection to get on the end of an inviting Frizzell cross before delicately guiding a right foot volley past Gallagher and high into the roof of the net.
Frizzell again turned provider just after the restart, his corner met by the head of Ethan McGee forcing a fantastic reflex save from the agile Gallagher.
Linfield doubled their lead on the hour, Frizzell capping a fine individual performance with his first goal of the season, getting on the end of a Dylan Wells cross to direct a header past Gallagher from close range.
At the other end, Chris Johns produced a fine fingertip save to deny Daniel Lafferty from a well struck free-kick in a rare Limavady United attack.
