The home side were bowled out for 230 late on day two of their two-day match in Chennai against Australia who had scored 241 in their first dig.
Australia were due to bat for another 45 minutes later on Wednesday to complete the match.
Uncapped No.4 batsman Ambati Rayudu hit a defiant 87 with nine fours and three sixes for India Board XI.
Henriques and specialist spinner Nathan Lyon claimed two wickets each as the home side slumped to 6-132. However Rayudu and Parvez Rassol (36) added 67 for the seventh wicket to steady the home side's innings.
Lyon finished with 3-69 off 13 overs while the uncapped Henriques was ever-dangerous and claimed 4-12 off 9.3 overs.
Western Australia's 19-year-old left-arm spinner Ashton Agar, who has been included in the squad as a net bowler and is heading home this weekend, was mobbed by teammates after removing Rassol caught at silly point by Glenn Maxwell at 7-199.
Henriques' four-wicket haul included the prize scalp of Rayudu who hit nine fours and three sixes from 150 balls.
Australia's other two allrounders -- spinners Maxwell (1-20 off four overs) and Steve Smith (0-34 off four) -- were unable to match the feats of Henriques.
Frontline pace trio James Pattinson (1-24), Jackson Bird and Peter Siddle took only one wicket between them although Bird was impossible to get away, conceding 10 runs from 10 overs.
Australia's Michael Clarke jogged laps of the oval and without any apparent concerns in an encouraging sign that the skipper can overcome a sore hamstring for the first Test starting on February 22.