Wicketkeeper batsman Brown’s 126 not out off 174 balls was a punchy captain’s innings to lead a recovery from 68 for four 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 for five from 96 overs. Yorkshire’s Jordan Thompson claimed three for 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 for three. 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 for four, 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 for two after 11. Medium pacer Brook’s first ball - 38 for three 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 for five 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.
Brown said: “I said last week that batting in front of a crowd makes a massive difference to my game. It’s just getting that natural tempo back. I was really appreciative of seeing a crowd in today. It was a fantastic day’s cricket. It was always going to be a tricky time, losing the toss with the lights on. We knew we’d have to work hard.
“But I thought the guys batted well before lunch even though we lost three wickets. That made it easier for me going in after lunch. I thought Dan (Ibrahim) was fantastic, and I’m so thrilled for him. I said to him walking off, ‘I got nought on debut, I was in and out and didn’t make an impact’. To go in against the second new ball and that bowling attack and get the score he did, I’m delighted."