After a drab first half, Championship side Ipswich took the lead when Frank Nouble capitalised on a defensive error just before the hour mark.
That was enough for the hosts to throw on Garner who scored a quick-fire double to put the League One side in front.
And while Ipswich got back level through their own substitute, David McGoldrick, there was no stopping Garner who won it in the 88th minute to dump the Tractor Boys out.
It took until the second half for the game to burst into life with the opening half a sluggish affair with few chances created by either team.
Town had the better of it but were unable to break down a stubborn Preston outfit, whose long balls were not finding targetman Kevin Davies.
Nouble managed to get in behind the Lilywhites defence at one point but none of his team-mates had made the run to get on the end of his inviting cut-back.
Ryan Tunnicliffe had the half's best chance when Stephen Hunt's corner was cleared to him but his effort was scooped harmlessly over the Preston crossbar from 18 yards.
Preston's best chance of the half came when Davies was inches away from connecting with Scott Laird's left-wing cross but the linesman's flag had already been raised.
Both sides stepped up a gear after the break and while Preston had the better of the exchanges it was the Championship side who took the lead.
It owed much to a terrible mix-up between goalkeeper Declan Rudd and defender Keith Keane, which allowed Nouble the simplest of finishes.
It did not take Preston long to introduce top scorer Garner in response and he provided the equaliser, heading home Paul Gallagher's corner through a crowd of bodies after 68 minutes.
Less than a minute later, after good work down the right from Chris Humphrey, Garner controlled Davies' knockdown and smashed his 12th goal of the season low past Scott Loach.
The Tractor Boys had their own leading scorer on the bench and shortly after his introduction, McGoldrick notched his 13th goal of the campaign when he planted home a close-range header from a Carlos Edwards cross in the 76th minute.
Ipswich had a glorious chance to take the lead when Paul Taylor fired the ball across goal only for Hunt to miss from six yards with the goal gaping.
Hunt was made to pay when Garner sealed his hat-trick by seizing on some more slack defending in the box to turn and fire home and send Preston through.
- Sports & Recreation
- Frank Nouble
- Kevin Davies
- David McGoldrick
- Stephen Hunt