Last weekend, Quins showed the resolve of champions as they mounted a Premiership record comeback from 27 points down to beat Wasps 42-40 in a sensational season-opener at Twickenham.
This time, O'Shea's men accelerated into an early 21-3 lead over Premiership new-boys London Welsh and then pulled clear to win 40-3 and claim another bonus point win.
Ugo Monye and George Robson scored two tries each before George Lowe and Ben Botica rounded off the victory with second-half scores.
"We are satisfied," O'Shea said.
"We held our discipline very well at times when it could have got quite fractious.
"I was delighted with the way we started, with the directness and the tempo we would want. You can't score six tries to nil and not be relatively happy.
"To get off to two bonus-point wins is a nice way to start the season."
Nick Evans, the architect of the comeback against Wasps, kicked all five of his conversion attempts and was named man of the match.
The New Zealand fly-half is considering his options for next season with clubs in Japan and France trying to tempt him away from The Stoop.
"Everyone at Harlequins wants him and hopefully he will be here," O'Shea said.
"We will do our talking behind the scenes."
Harlequins were forced to stage the game on a Friday night because Lady Gaga is taking up a two-night residency at Twickenham, just over the A316, this weekend.
That was particularly tough on Premiership new-boys London Welsh, who were forced to face the reigning champions just five days after their top flight debut against Leicester.
"Tonight wasn't a good day in the office. We knew it would be a tough game but we were keen to perform better than we did tonight," said London Welsh director of rugby Lyn Jones.
"The disappointment was not losing but not justifying how well we can play. The boys are devastated at the moment.
"We suffered a bit from Harlequins' poor start last week. They came hard at us.
"We have got boys who are learning to deal with the speed and the intensity of the Premiership. We are hoping to adjust as quickly as we can."
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