Root came in at 199-2 in the day’s fifth over and hit 12 fours in 127 balls before edging fast bowler Henry Crocombe behind during the latter stages of the afternoon session.
Sussex struck three times in the morning, with Yorkshire 300-4 at lunch.
Fynn Hudson-Prentice’s seam angled one back into left-handed Bean and trapped him lbw for the addition of only four more runs to his overnight tally.
The left-arm spin of James Coles, who later took the second new ball, bowled Jonny Bairstow through the gate for six, uprooting his middle-stump.
Sandwiched in between, Whiteman was caught behind off Crocombe.
Yorkshire-born Western Australia captain Whiteman, playing for his birth county as a local for the next three seasons, had reached his century with a drilled straight six off Coles, getting there off 188 balls.
Root was at ease against seam and spin, including emerging twirler Coles and his former seam-bowling England team-mate Ollie Robinson.
It looked inevitable for much of his innings that he would reach three figures.
This was his first first-class innings in 109 days since his second innings of January’s Ashes Test Match at Sydney, and it was also his fifth 50-plus score in seven Championship innings for Yorkshire dating back two years to the day.
Sussex plugged away for reward in benign conditions. Without ever looking like blowing Yorkshire away, they chipped away and claimed wickets at regular intervals.
In fairness, they were a bowler light having lost seam-bowling all-rounder Tom Price to a sprained right ankle which he suffered whilst fielding the day’s second delivery at deep backward square-leg.
The visitors opted not to utilise the ECB’s substitution rule, but he was off the field all day.
Root reached his fifty off 59 balls before lunch and was within touching distance of raising his bat once more when Crocombe got one to bounce more than expected, with the England man feeling for it outside off-stump and edging behind to John Simpson. In all, he hit 12 fours.
With Matthew Revis having earlier fallen to Coles – he and Root shared a fifth-wicket 86 – Yorkshire were 395-6 during the second half of the afternoon.
Dom Bess was trapped lbw by the miserly medium pace of Tom Haines before George Hill, who posted 50, chipped Jack Carson’s off-spin to midwicket – Yorkshire were 457-8 at tea.
Yorkshire’s overseas quicks Logan van Beek and Jhye Richardson then contributed 29 and 35 respectively – they shared a ninth-wicket 49 – to help their side into the lead.
Van Beek edged Crocombe behind and Richardson was bowled attacking at Coles.
Both bowlers finished with three wickets before Australian Richardson, who struggled with the ball at the start of the game, bowled compatriot Daniel Hughes with a beauty in the third over the Sussex second innings.
Haines then chipped a return catch to Hill just before close, setting up an interesting fourth morning at least.
Report by ECB Reporters’ Network, supported by Rothesay.
