Wales flanker Martyn Williams crossed for their only try while Ireland fly-half Ronan O'Gara booted nine points in a tense encounter which was thrown wide open by Isa Nacewa's 62nd minute touchdown.
The Lions, hampered by the early loss of in-form fly-half Charlie Hodgson to injury, were put under tremendous pressure in the final quarter but kept their nerve with O'Gara's boot proving effective.
Hodgson settled the Lions' nerves with an early penalty and then carved Auckland wide open with an arcing run, but his ensuing kick was cleared under pressure by winger Nacewa.
Auckland's ball supply was being restricted by poor line-out throwing from hooker Semisi Telefoni - their third-choice number two thanks to All Black call-ups - while sloppy handling errors were also taking their toll.
Gordon D'Arcy prevented Joe Rokocoko from squeezing in at the right corner and Auckland maintained the pressure with powerful prop John Afoa barging over, only to have the try disallowed following television replays.
The Lions were slowly surrendering the initiative and their cause was net helped by an injury to Hodgson, who limped off after taking a heavy knock, with O'Gara coming on as his replacement.
Denis Hickie wasted a glorious chance by spilling a cross-field kick from O'Gara, who then slotted a penalty, but the score was quickly cancelled out by three points from the boot of Brent Ward.
Auckland then started to buckle and their defence cracked two minutes before half-time when a scintillating run from Mark Cueto swept the Lions upfield before the scoring pass was supplied by Matt Dawson to Williams.
Ward kicked his second penalty and then converted a 62nd-minute try from Nacewa, who finished off a move begun by fly-half Tasesa Lavea, slicing the Lions' lead to a single point.
Ward saw a 70th-minute penalty strike the right post before O'Gara showed the Auckland full-back how it was done, extending the Lions' points cushion to four points as the tourists held out for victory.