Boudweijn Zenden, in his first appearance since suffering cruciate ligament damage last November, shot wastefully wide from Gerrard's pass four minutes after the interval, the winger's last meaningful action before being replaced by Luis Garcia.
Maccabi, though, were comfortable and came close to regaining the lead on 61 minutes when Colautti rose above Steve Finnan at the far post to head just wide.
But Liverpool were gradually gaining momentum and wrested control of the game in the final half-hour. Crouch, on for Bellamy, nodded at goalkeeper Davidovitch and then headed a Finnan cross narrowly wide.
No home player was on hand to apply the finishing touch to some Garcia trickery, and then Davidovitch produced a fine save to keep out Pennant's deflected free-kick from 20 yards before Garcia had a decent shout for a penalty waved away by referee Stark.
That seemed to be that, until Gonzalez, two minutes after coming on, drifted in unmarked at the far post to control Alonso's deep pass and deliver an expert finish beyond the onrushing Davidovitch.
There was still enough time for Reina to have to make a smart save with his legs to deny Colautti, more evidence the tie is very much alive when the second leg takes place in 13 days' time.
Benitez's side will discover by tomorrow lunchtime just where that game will be held, with Kiev the most likely venue.
What's for certain is that, no matter where the game is played, Liverpool will have to play a lot better than this to progress. Perhaps, as Gonzalez discovered, the best things will come to those that wait.
MAN OF THE MATCH: Mohamed Sissoko - The Mali international delivered a performance of trademark perpetual motion, and was unfortunate to pick up a booking
LIVERPOOL: Reina, Finnan, Carragher, Hyypia, Riise, Gerrard (Gonzalez 85), Sissoko, Alonso, Zenden (Luis Garcia 55), Pennant, Bellamy (Crouch 65). Subs: Dudek, Kromkamp, Paletta, Peltier. BOOKED: Sissoko (foul).
MACCABI HAIFA: Davidovitch, Harazi, Olarra, Keinan, Magralishvili, Boccoli, Anderson, Xavier, Masudi (Meshumar 90), Colautti, Katan (Melicsohn 85). Subs: Al Madon, Kanan, Swan, Hemad, Gazal.
BOOKED: Magralishvili, Colautti (fouls).
REFEREE: Wolfgang Stark (Germany). ATT: 40,058
NEXT GAME: Liverpool v Chelsea, FA Community Shield, Sunday August 13, 3pm
