The Nerazzurri started brightly with Francesco Forte firing home on 19 minutes before Kristian Adorjan levelled for Liverpool from the penalty spot just after the half-hour mark.
Inter snatched the lead from the Reds just before the break through Nicolo Belloni who found the net with a neat finish.
With 10 minutes left to play, Garritano capped a swift Inter move by beating Tyrell Belford in the Liverpool goal to extend their lead to 3-1. Adorjan grabbed a late consolation goal for Liverpool to end the tie 3-2.
Aston Villa faced Celtic at Villa Park in a Battle of Britain in Group 4. Villa took the lead through Samir Carruthers who finished off a well worked move after 20 minutes. Celtic took a while to settle into the game with the Villans setting the early tempo and keeping the ball well.
The home side took advantage of their dominance in possession by extending their lead on the half hour mark through Malcolm Melvin who slotted past Leonardo Fasan from all of 20 yards.
After the break, Celtic came out looking far sharper and were the more dangerous side in the second 45. Just four minutes into the second half Jackson Irvine found the net to make it 2-1.
For all their efforts and chances Celtic couldn't find the equaliser with their closest effort coming from substitute Denny Johnstone who hit the post. Aston Villa move above Celtic in Group Four having played a game more.
Meanwhile at the Aker Stadion, Viktor Fischer scored a brilliant hat-trick against Molde to give Ajax a winning start in this season's competition.
Fischer looked a threat from the first whistle, getting in behind Molde's backline and finding good positions around the box.
It was Lesley de Sa who opened the scoring on 14 minutes with a fine strike, shortly before Fischer slotted past Ola Opheim to make it 2-0 to the visitors after 20 minutes.
Fischer scored two more goals in the second half and completed his hat-trick 10 minutes before time. Sporkslede made it 5-0 in added time to send Ajax second in Group 3 behind CSKA Moscow.
Juventus secured their first win in the NextGen Series with a 2-0 win over French giants Paris St.Germain in Turin. The hosts took the lead on 57 minutes through midfielder Giuseppe Ruggiero before Brazilian striker Leanardo Bonatini made it a more comfortable win for the hosts slotting home in added time to make it 2-0.
- Aston Villa