Kent 265 and 33 for 2 (Bell-Drummond 24*) need another 412 runs to beat Yorkshire 379 and 330 for 5 declared (Lyth 116, Root 101, Brook 66*)
Joe Root scored a century to put Yorkshire in a commanding position after day three of their LV= Insurance County Championship game with Kent at Canterbury, the visitors needing eight wickets for victory after declaring their second innings on 330 for 5, setting Kent an improbable target of 445.
The hosts were reduced to 33 for 2 at stumps and trailed by 411 in the Group Three fixture, Jordan Thompson taking 1 for nought David Willey 1 for 15.
England batsmen past and present starred for the visitors, with former opener Adam Lyth hitting 116 and current skipper Root making 101 in their second innings. Kent's Joe Denly took 2 for 61, while Matt Milnes claimed 2 for 68.
Yorkshire resumed on 6 for nought, and although Kent bowled well for the first hour, their only success during that time came when Grant Stewart had Tom Kohler-Cadmore caught at first slip by Jordan Cox for 3.
Milnes trapped Tom Loten lbw for 21, shortly before lunch, but an attack shorn of the injured Harry Podmore struggled to make any impact during a truncated afternoon session.
Lyth was on 85 when he edged Milnes to slip, but Zak Crawley missed a difficult chance and, having made 97 in his first innings, Lyth emitted a howl of joy when he reached his century with a four off Miguel Cummins.
The visitors had moved on to 171 for 2 when play was suspended between 2.50 pm and 4.10 pm while the funeral of HRH Prince Philip took place.
Lyth eventually fell to Milnes, caught at first slip by Cox, ending a stand of 119 for the third wicket. Harry Brook then joined Root and scored rapidly to set up the declaration, making an unbeaten 66 that included a reverse-swept four.
Root was bowled by Denly and Yorkshire declared when the same bowler bowled Thompson for 6 in his next over, forcing Kent to face 12 hazardous overs before stumps.
Willey subsequently yorked Cox for a duck and Crawley was caught by Lyth at slip off Thompson, leaving Daniel Bell-Drummond and night-watchman Milnes the not-out batsmen on 24 and nought at the close.
"I've changed a few things technically," Root said. "I haven't had the opportunity to face a lot of seam (over the winter), I've faced a lot of spin, so for me to spend some time in the middle was really important.
"Adam's in cracking form, I think he's played lovely and let's be honest, he pretty much saved us single-handedly last week. In the first innings it looked like he was batting on a completely different wicket to the other guys, he was hitting it so fluently. You need your senior players to step up and lead the way for what is still a young team.
"It was brilliant to get a couple of wickets before the close of play. We've had three very good days but we've got to follow it through tomorrow."