Substitute Paul McShane stabbed home a late but fully deserved winner at the Aesseal New York Stadium this afternoon as Jaap Stam's side earned all three points against a rejuvenated Rotherham side beginning life under new boss Kenny Jackett.
A brilliant goalline save from Ali Al Habsi denied Richard Wood at one end, before Lee Camp saved a Garath McCleary penalty won by Joey van den Berg at the other in an open second half. Swift struck the crossbar with a superb effort and Reading were by far the better side in a second half in which they relentlessly pressed for a winner - and it came in the form of McShane's late, late strike.
Jaap Stam included Academy graduate Liam Kelly amongst his starting eleven for the first time at the Aesseal New York Stadium, starting him in midfield while also reintroducing Jordan Obita to his line-up at left-back - in a squad that included five Academy products.
And the Royals began the brighter in the opening minutes, McCleary crossing for Kermorgant in the middle but a defender nodding clear, then Kelly taking aim from distance but seeing his effort charged down and looping into the arms of Lee Camp.
But the Millers posed some early problems with inswinging corners that Al Habsi did well to punch clear amongst a crowd. And the Omani stopper raced off his line to pat the ball off the head of centre-half Richard Wood moments later.
McCleary had the first meaningful effort at goal though, collecting a crossfield ball from Swift, cutting inside from the right and drilling just wide of the bottom right corner with his left foot. Al Habsi was called into action to push Jon Taylor's effort around the post at the other end though as an open game found its tempo.
Long throws and balls into the box were Rotherham's route to goal and they were causing Reading's defence some problems - a couple of times the second ball nearly dropping kindly for the hosts inside the six yard box. The visitors meanwhile tried to use the pace of McCleary to get in behind but Fry held him off as he tried to scamper onto a Swift throughball.
Swift went close, fizzing a 25-yard effort wide of the right post. Beerens drilled off target soon after. Reading were beginning to assert their authority but unable to break down a disciplined Rotherham defence. And although the home side barely had a kick of the ball in the last ten minutes of the half, the game remained goalless at the break.
Half-time: Rotherham 0-0 Reading
The first half began in the same pattern before an almighty goalmouth scramble ensued in front of Ali Al Habsi's goal. The upshot was a booking for Chris Gunter and Dexter Blackstock.
And United came very close to opening the scoring ten minutes into the second period when Wood rose high and powered a header goalwards which was somehow clawed off his goalline by the brilliant Al Habsi.
Al Habsi came to the rescue moments later too, coming off his line to narrow the angle as Ward got in behind the Royals back line and went through on goal, saving with his body as the Rotherham striker took aim. A brilliant sliding block from Kermorgant thwarted the home side next, as Kenny Jackett's side came out of the blocks quickly.
But Reading had a golden opportunity to break the deadlock on the hour. Swift's one two with Van den Berg found the Dutchman thundering into the box and he was sent tumbling by a stray Rotherham defender's leg. Garath McCleary stepped up but Camp saved with his legs to keep the game goalless.
The game had opened up and Reading broke very well down the right through Williams who found Gunter and his low cross was flicked into the side netting by Kermorgant at the near post.
Beerens arrowed just wide next, then he beat a man down the right to supply a lovely cross for Kermorgant who connected sweetly with a first time volley but watched as it skidded inches wide of the right upright.
Jaap Stam's men were starting to lay siege to the Rotherham goal as the hosts tired, Obita bursting down the left next and pulling it back for Kermorgant who's shot was charged down and hacked clear with 15 minutes remaining.
Swift came even closer to a goal when he scuttled across the edge of the area and unleashed a wonderful strike that beat Camp completely but cannoned into the crossbar to the travelling fans' angst.
Time was running out. Kermorgant found the run of McCleary with a deft flick but his left-footed effort was saved by the dive of Camp. Then Gunter's low cross on the counter was cleared off the toes of Beerens.
But with five minutes of the match remaining, Reading found the goal they deserved. Beerens arced a shot towards goal, Camp could only palm it away from underneath his crossbar and it dropped to PaulMcShane who chested it down and stabbed the ball high into the Millers net on the volley.
It took some good goalkeeping from Al Habsi to prevent Jackett's men from finding an immediate response though. He raced off his line to save at the feet of Ward and then regathered his feet to claw the ball away from the following up Forde.
Five minutes of injury time were signalled and Frecklington volleyed wide after Reading had cleared another dangerous corner.
Full-time: Rotherham 0-1 Reading
Rotherham: Camp, Mattock, Halford, Wood, Frecklington (c), Taylor, Fisher, Fry, Newell (Brown 64), Blackstock (Forde 74), Ward.
Subs: Price, Vaulks, Forster-Caskey, Ball, Belaid.
Yellow: Blackstock, Halford.
Reading: Al-Habsi, Gunter (c), Obita, L.Moore, Van den Berg, Kelly (McShane 28), Swift (Evans 89), Williams, Beerens, McCleary, Kermorgant.
Subs: S.Moore, Watson, Gravenberch, Blackett, Samuel.
Goals: McShane (86)
Att: 8,800 (644 away)