Former Fulham man Pavel Pogrebnyak sprung the offside trap and dinked a delicate chip over County goalkeeper Lenny Pidgeley to open the scoring.
Striker Nick Blackman doubled the lead for the Championship side with a solo effort before Shaun Jeffers' header gave League Two Newport hope.
Seconds after coming on for his debut striker Craig Tanner made it 3-1.
Newport County manager Justin Edinburgh told BBC Radio Wales:
"I thought we needed a reaction after our performance on Saturday and certainly got that from the players.
"I thought from start to finish we gave a good account of ourselves and ran Reading hard.
"We had nothing to lose second half and I felt we deserved the goal that we got at the end."
Reading coasted into the second round of the Capital One Cup at the expense of Newport County.