After winning the toss and batting, NSW went to stumps well placed at 4-345, with Patterson (117no off 209 balls), Konstas (71 off 142), Lachlan Shaw (61 off 107) and Ollie Davies (52 off 58) all posting important knocks.
Patterson brought up his 16th first-class century late in the day when he fended Jhye Richardson (2-78) through the off-side.
The 33-year-old's only two Tests came in 2019, posting scores of 30 and 114no against Sri Lanka for an average of 144.
And with the Australian Test team's batting line-up by no means settled, Patterson's century - following on from his knock of 54 in NSW's Shield opener - comes at the perfect time.
Konstas is also aiming to put his name back in the Test selection mix.
The 21-year-old, playing his first Shield game of the season, was looking the goods on Monday until he skied Liam Haskett (2-58) attempting a pull shot.
Konstas only averaged 33 from his 10 Shield matches last season but his knock against WA has raised hopes he can again push his name up in lights.
The opener also scored 67 while playing for Australia A against India A in a one-day match earlier this month.
Konstas burst onto the international scene with an impressive Boxing Day Test debut against India in 2024, but he hasn't been seen in the baggy green since July last year after a lean run.
WA posted a two-wicket victory over Queensland in their opening match of the Shield season.
But they struggled to make a dent into NSW's powerful line-up on Monday on a batter-friendly deck, with Patterson thriving on the way to his unbeaten century.
