Everyone inside Deepdale stood to applaud in the seventh minute in tribute to Tranmere midfielder Joe Thompson who was diagnosed with cancer this week.
Kevin Davies fired over the Rovers crossbar but Preston's best chance of the first half came when Keith Keane burst through into the penalty area, forcing Tranmere goalkeeper Owain Fon Williams into a save.
A 63rd-minute Preston corner was then headed over by former Bolton striker Davies, who endured a frustrating afternoon and was hauled off shortly after.
Jake Kirby's intelligent pass then sent Tranmere top scorer Ryan Lowe through on goal but Rudd saved the shot with his feet.
And it was to prove vital as Garner notched his second league goal of the season on the stroke of full-time, heading home Chris Humphrey's cross.
- Sports & Recreation
- Kevin Davies
- Declan Rudd