Rotherham were the better side for much of the first half but Reading poached a 41st-minute half-time lead through Yakou Meite.
Although Rotherham again threatened in the second period, Reading proved resilient and added further late goals from Meite and top scorer Lucas Joao.
Manager Warne, returning to the touchline after a two-game absence as he self-isolated at home due to family members contracting Covid-19, bemoaned his side’s failure to capitalise on their early superiority.
“I thought that we played really well, especially in the first half,” said Warne.
“We must have about 70 per cent possession then.
“But we just didn’t create enough clear-cut opportunities to take the lead.
“Virtually the first time that Reading went into our box – in the 41st minute – they took the lead. It was a very harsh lesson.
“And it was their first shot. Wow! I’m not sure if that makes me feel better or worse.
“Going in at half-time was pretty hard but I was pretty pleased with how we were playing.
And I still think that we started off the better in the second half.
“I put two up front and we had a couple of chances but didn’t take them.
“We then went three up front and it was ‘kitchen sink’ time then.”
Reading were fortunate not to concede an equaliser through Rotherham substitute George Hirst.
With his first touch after coming on, Hirst sent a firm shot goalwards, only for home skipper Liam Moore to clear it off the line.
Reading then as good as sealed their sixth win of the campaign in the 79th minute. Moore helped on a Michael Olise corner and Meite pounced with a spectacular overhead kick to beat Blackman.
In stoppage time, Rotherham defender Michael Ihiekwe brought down Lucas Joao and the former Sheffield Wednesday man notched his seventh goal of the season from the spot.
Reading have now six of their seven league games this season, drawing the other,
Reading: Cabral, Esteves, Morrison, Moore, Richards, Rinomhota, Laurent, Meite, Semedo (McIntyre 80), Ejaria (Olise 66), Puscas (Joao 66). Unused substitutes: Gibson, Southwood, Aluko, Tetek.
Rotherham: Blackman, Harding (Ladapo 71), Ihiekwe, Wood, Mattock, Shaun MacDonald, Jozefzoon (Olosunde 64), Lindsay (Hirst 62),Barlaser, Wiles, Smith. Unused substitutes: Johansson, Jones, Sadlier, Crooks.
Referee: M Donohue (Sale).
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