Joseph touched down for the first try and then played a key role in those scored by David Paice and Topsy Ojo before Jamie Gibson wrapped up the bonus point with a 39-17 success.
The Exiles opened a 33-3 lead before Northampton, who had been unbeaten before Saturday's game, worked late consolation tries for Ken Pisi and Phil Dowson.
Joseph made his Test debut during England's summer tour of South Africa and London Irish director of rugby Smith said: "I would like to see JJ get another crack.
"He is a class act and his talent is well regarded by the English coaches.
"And with Mike Catt (the former London Irish player and coach) now part of the England set-up, he knows what JJ can do."
There was nothing before the match to indicate a London Irish victory was on the cards from a side languishing 11th in the Premiership.
The Exiles defence had conceded an average of 36 points a game up until this match, with only Sale suffering a worse start to the campaign.
In complete contrast, Northampton arrived in Reading as guardians of the only unbeaten record left in the competition but they were without injured captain Dylan Hartley.
London Irish met the Saints forwards head on and set the platform for the likes of Joseph and Steven Shingler to shine.
"It was a big challenge for us because confidence wasn't high," Smith said.
"The boys really fronted up today. They got no change out of us at scrum time and in the lineout drive and we have a lot of class in the back line."
Furious Northampton director of rugby Jim Mallinder blasted his side's performance as embarrassing and unacceptable.
"There was no intensity there from us, our accuracy in just about everything we did that first 60 minutes was awful," Mallinder said.
"Mentally, if you underestimate any team in the Premiership then you will get turned over and that is what happened. Mentally we weren't up for today's game and that showed.
"As a group we are all very disappointed. We embarrassed ourselves.
"The talk in the week had all been about how difficult this game was going to be, how desperate London Irish would be, how we should not be looking to give their outside backs any ammunition.
"We had to get our set piece right and defend with intensity - all those things we talked about didn't happen this afternoon.
"We embarrassed ourselves today, we let ourselves down with a performance that was not acceptable."
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