The midfielder and summer signing scored twice in the final 10 minutes after Dave Edwards' 73rd-minute header had given the visitors the lead.
Saville's two goals came five minutes apart, following a largely-uneventful affair which looked set to be decided by a solitary goal, and that ensured Reading are without a win in five.
Millwall have made a promising start to their first season back in the Championship and are now 12th after 10 games.
When asked about Saville, Millwall manager Harris said: "He's been buzzing (at receiving that call-up). We saw that, that spring in his step.
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"Of course I'll be nervous about (my internationals) being injured, but when my players come back from international duty, they come back on cloud nine, so I'm really looking forward to their opportunity for them.
"Just when you were thinking about getting more quality on the football to hurt them, we conceded a poor goal.
"The goals were good, but the belief is the key. At this level, against good sides, to come from a goal down is a big ask. They've built that belief during the last six weeks with their performances.
"Our discipline, organisation and shape was magnificent; our patience.
"I couldn't see Reading scoring, and we didn't particularly trouble their goalkeeper either. I'm really pleased for George. He deserved his goals.
"We're still in that transition period (from League One to Championship). But beating Norwich, beating Leeds, beating Reading, three big clubs at this level, shows we so far well and truly deserve to be here. After Barnsley (on Saturday), we can look at ourselves in the international break and say 'How well have we done?' But I'll certainly praise them for what they've achieved so far in the first 10 games of the season.
"I've got some players in that dressing room playing the best football of their careers."