In reply to West Indies' first-innings total of 188, Australia went to lunch at 5-144 on Thursday at Adelaide Oval.
Travis Head is unbeaten on 41 with Alex Carey nine not out after the Australians lost three wickets in the opening session.
Travis Head reached lunch on day two of the first Test against West Indies unbeaten on 41. (Matt Turner/AAP PHOTOS)
Joseph removed Cameron Green for 14, Khawaja was dismissed for 45 and Mitchell Marsh went for five.
After resuming at 2-59, Green struck Joseph for consecutive boundaries early on but was dismissed next ball - the 11th of the day.
The right-hander pushed forward defensively to a good length delivery but edged to wicketkeeper Joshua Da Silva.
The wicket gave Joseph figures of 3-26 after dismissing Steve Smith (12) and Marnus Labuschagne (10) on the opening day.
Khawaja and home-town hero Head put on 46 runs but the stand ended when the opener became debutant Justin Greaves's first Test wicket.
Khawaja slashed at a wide, full ball and got a thick edge which was smartly caught by Alick Athanaze, diving to his right at second slip.
The dismissal continues a string of solid but not spectacular scores for Khawaja who, since a century against against England last June, has been out six times in the 40s.
Head made a tentative start to his knock and, on 10, almost chopped-on to his stumps when attempting a drive off Kemar Roach.
The aggressive left-hander found some fluency amid some uncertainty in his 61-balls before lunch, hitting four fours and smacking medium-pacer Greaves over square leg for six.
West Indies celebrate the dismissal of Mitchell Marsh (left) shortly before lunch. (Matt Turner/AAP PHOTOS)
Marsh fell about 15 minutes before lunch, a victim of shrewd captaincy from Kraigg Brathwaite.
The West Indies skipper deployed Greaves at a short third slip to the bowling of Roach.
Marsh nicked one ball just short of the helmeted Greaves and, next ball, edged again and was superbly caught low-down. Â
Paceman Joseph, who made 36 batting at No.11 - the second-highest score in the visitor's innings - had figures of 3-52 at the break with Greaves on 1-18 and Roach 1-36.
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