Green's (197) epic innings was brought to an end when trapped in front by Sean Abbott, as WA were all out for 534 shortly before lunch on the final day.
With NSW 2-107 at tea after compiling 6(dec)-443 in their first innings, the sides agreed no result could be achieved and called off the match with a session remaining.
Cameron Gannon and Ashton Agar took a wicket apiece, while Daniel Hughes (2) and Kurtis Patterson (48) were the men out for the Blues. Nick Larkin (33) and first innings centurion Moises Henriques (15) were the not out batsmen.
Earlier in the day, having resumed unbeaten on 28, Matt Kelly flayed the Blues attack and bludgeoned 61 from 43 balls including four boundaries and six sixes to also record his highest first-class score.
While the match at Adelaide's Gladys Elphick Park fizzled out, interest in Green remains high.
"It’s probably an innings I’m most proud of, especially how hard they came all day really,” he said.
“It was pretty flat and in the batter’s favour but they came pretty hard so I’ll take a lot out of it.”
Allrounder Green didn't bowl for much of 2019-20 and has yet to pick up the ball in a match this season because of stress fractures in his back, but he is pushing for a bowling return.
“We’ll have a few training sessions over the next few days that I’ll bowl at and we’ll see how it’s progressing and if I can bowl in the game," he said.
Alongside his 438-ball innings against NSW, Green scored 699 runs at 63.54 during the last Sheffield Shield season.