Centre back Matt Miazga struck deep into stoppage time as the game appeared to be petering out into a goalless draw.
Victory sees the Royals move two points clear of the bottom three as they ended a winless league run dating back to August 24.
Bowen, 55, took over on Monday – his first permanent role as a manager – to replace the sacked Portuguese Jose Gomes.
Previously Reading's sporting director, he had spent most of his 20-year coaching career as number two to fellow former Wales international Mark Hughes.
Bowen inherited a team that were without a win in six league matches, including five defeats, under Gomes.
Preston, meanwhile, came into the match in third place in the table and were unbeaten in eight Championship games, winning five of them.
The visitors began the brighter, with full-back Andy Hughes causing problems when going forward on the left flank.
Preston continued to press but a dangerous free-kick from captain Paul Gallagher narrowly missed all the bodies in a crowded home area.
Reading finally got going in attack, with left-back Jordan Obita releasing striker George Puscas, but the Romania international tried an ambitious volley from a tight angle that flew over the crossbar.
Preston responded when Barkhuizen set off on a mazy run along the right flank, only to finish with a weak effort at Rafael.
Pele replied for the hosts, sending in a superb low centre into the North End six-yard box. Puscas arrived to meet it but could manage only the slightest of touches and the chance went begging.
Reading upped the tempo before half-time but Rudd made solid saves to twice deny Ovie Ejaria.
Preston launched a rare attack early in the second half and should have gone in front.
Ejaria again proved troublesome for Preston but he sliced over a clear opportunity from an Andy Yiadom centre.
But Reading snatched it at the end when Miazga followed up to net from close range after Rudd have saved from Jordan Obita.