Oli Page scored the late winner that earned Liphook, former cup winners, a home meeting with Alresford in the last eight.
Infinity led for much of the match after taking an early lead through Terry New. But Steve Harding equalised on the hour-mark and Page struck in the 80th minute to complete a fine Liphook fightback.
Clanfield will travel to the winners of the Hayling/Montefiore Halls tie in their quarter-final on February 3.
Clanfield lost 4-2 at home to Stockbridge in the Hampshire Premier League last weekend. Liss Athletic also went down, beaten 3-1 at Overton.
In Division? One, Headley lost 3-0 at high-riding Netley Central.
Toby Wallace and Ben Coverdale scored the goals as AFC?Petersfield beat bottom side Michelmersh 2-0.
The game between Upham and Four Marks was postponed due to damage to the pitch caused by joyriders.