Wicketkeeper batsman Brown’s 126 not out off 174 balls was a punchy captain’s innings to lead a recovery from 68-4 shortly after lunch.
Sussex are fielding two debutants - 20-year-old opener Ali Orr, who made 15, and all-rounder Dan Ibrahim. Aged 16 years and 298 days, Ibrahim is the second youngest player to represent the county.
Under a grey sky with the floodlights on until early afternoon, the Hove side could have crumbled but impressively closed on 267-5 from 96 overs. Yorkshire’s Jordan Thompson claimed 3-42.
Brown shared 107 for the fifth wicket with Aaron Thomason from early afternoon until early evening and later 92 unbroken with Ibrahim, who finished with 37 not out.
Thomason was far more reserved for 40 off 181 balls as batting conditions eased through the day.
Yorkshire edged the opening session after Steve Patterson won his seventh toss in eight Championship games, restricting Sussex to 63-3. David Willey, Thompson and Harry Brook claimed the wickets.
When Thompson struck again in the second over of the afternoon to get Australian Travis Head caught behind and leave the visitors at 68-4, three wickets had fallen in the first over of a bowler’s spell.
Willey made the breakthrough in the fourth over when he had Tom Haines caught at third slip before Thompson had Stiaan van Zyl caught behind in his first over to leave Sussex at 25-2 after 11.
Medium pacer Brook’s first ball - 38-3 in the 23rd - then saw left-handed Orr carelessly pick out long leg.
Brown drove handsomely against seam and spin on the way to a 60-ball fifty, and 8,000 career first-class runs, in front of Headingley’s first crowd (2,056) for a men’s first-team game in 623 days.
His stand with Thomason was broken when Thompson had the latter chipping to midwicket.
At 175-5 after 71 overs, Ibrahim strode to the crease and followed in the footsteps of James Coles, who debuted last summer aged 16 years and 157 days.
Ibrahim got off the mark with a clipped two first ball and looked extremely composed.
Brown brought up his first century in two years off 149 balls inside the final 50 minutes of play.
Support The Yorkshire Post and become a subscriber today. Your subscription will help us to continue to bring quality news to the people of Yorkshire. In return, you’ll see fewer ads on site, get free access to our app and receive exclusive members-only offers. Click HERE to subscribe.