The Royals followed up last week's win over West Ham by claiming another prized scalp.
Church produced a quality finish into the top corner after controlling Jobi McAnuff's pass inside the penalty area with only one minute and 53 seconds on the clock.
Leeds, without injured skipper Jonny Howson, enjoyed plenty of possession but lacked guile where it mattered and rarely opened up the visitors' solid defence.
Simon Grayson's side remain in sixth place on goal difference despite a fourth home league defeat of the season, while Reading, having steadily climbed the table virtually unnoticed in recent weeks, have cut the gap on the Yorkshiremen to two points.
Leeds goalkeeper Andy Lonergan returned to the starting line-up as on-loan Alex McCarthy was not allowed to play against his parent club, while striker Ross McCormack and midfielder Michael Brown were also recalled.
Reading midfielder Hal Robson-Kanu, defender Andy Griffin and Church returned to the visitors' starting line-up.
Church wasted little time in chalking up his sixth goal of the season in Reading's first attack.
The Wales international, 23, collected McAnuff's ball into the penalty area and planted a perfect angled finish beyond Lonergan and into the top corner from 12 yards.
Leeds went in search of a quick riposte and monopolised possession without creating a clear opening before McAnuff pulled a shot from the right edge of the area wide following a swift Reading counter-attack in the 13th minute.
McAnuff was denied by Lonergan's sprawling save seven minutes later as the visitors threatened to increase their lead and Kaspars Gorkss headed Mikele Leigertwood's free-kick over the crossbar as half-time approached.
For all Leeds' possession they failed to fashion a single attempt on goal until McCormack headed straight at Reading goalkeeper Adam Federici in time added on at the end of the first half.
Reading continued to keep Leeds at arm's length after the restart, but home midfielder Danny Pugh went close to an equaliser in the 59th minute when his angled drive from inside the area was well saved by Federici.
Royals midfielder Jem Karacan was forced off injured and replaced by Jay Tabb moments later, while Leeds manager Simon Grayson made three tactical substitutions in the 65th minute in an effort to break out of Reading's stranglehold.
Striker Andy Keogh and midfield pair Mika Vayrynen and Lloyd Sam replaced Adam Clayton, Brown and McCormack.
Keogh lashed a shot from inside the area over the crossbar within a minute of coming on following Snodgrass's free-kick, but as Leeds probed Reading almost snatched a second when defender Alex Pearce headed wide from just six yards.
Pearce then rescued his side at the other end when deflecting Leeds midfielder Pugh's goalbound shot from 25 yards for a corner, but it was as close as the home side were going to get to rescuing a point as Reading comfortably held on.
