Preston took just six minutes to go in front as Chris Humphrey superbly controlled Jack King's long pass and saw his angled shot from 14 yards deflected into the far corner.
Oldham midfielder David Worrall fired off target from a good position, but Paul Gallagher and Tom Clarke both had chances for Preston.
Adam Lockwood and Jonson Clarke-Harris went close for the home side before visiting goalkeeper Declan Rudd pulled off an excellent stop from Korey Smith.
After weathering Oldham's best spell, Preston doubled their lead in the 71st minute as Humphrey again caused problems down the right and set up Garner for a two-yard tap-in.
Oldham responded four minutes later when Gary Harkins controlled Worrall's header and lashed the ball into the top corner from 12 yards.
The Latics went down to 10 men in the 78th minute when Clarke-Harris was shown a straight red card for handling Garner's header on the goalline.
Garner's resulting penalty was brilliantly saved by Mark Oxley, but the Preston forward bagged his second goal two minutes from time with a dipping 20-yard shot which bounced in off the post.