Warwickshire 455 (Dawson 5-146) and 46 for 0 (Davies 34*) lead Hampshire 365 (Gubbins 119, Middleton 116) by 136 runs
Fletcha Middleton celebrated his maiden Vitality County Championship century but Hampshire and Warwickshire look likely to draw at Utilita Bowl.
Homegrown Middleton, impressive in last season's Metro Bank One Day Cup, amassed 116, having put on 213 runs for the second wicket with fellow centurion Nick Gubbins.
An afternoon collapse saw Hampshire lose five middle-order wickets for 45, which put Warwickshire on course for a 90-run first-innings lead.
Rob Yates - who now has 296 runs and 11 wickets this season - and opening partner Alex Davies reached 46 without loss by close - a lead of 136.
Middleton's father Tony had scored his maiden first-class century, against Kent, in this week 34 years ago - he would end that season with 1,238 runs for Hampshire. Fletcha will be hoping to replicate that.
There were plenty of similarities. Kevan James and Simon Hinks were in attendance on both occasions; now commentator and match referee. But most notable was the steeliness about the innings.
Tony's would see him score 127 runs in 314 balls across just over six hours. Fletcha kept up the family tradition of crease occupation over quick scoring; his eventual 116 came in 329 balls in four minutes shy of seven hours.
For large periods of the morning session the scoreboard seemed to be stuck. Only 10 runs were scored in the first half an hour, with 80 runs spread out before lunch. Middleton and Gubbins are hardly Bazball enthusiasts at the best of times but an idle pitch didn't help.
Gubbins followed up his two half-centuries against Lancashire last week with a 216-ball century - his 17th of his first-class career and his seventh since arriving at Hampshire two and a half years ago.
After a session of nothingness, best summed up by a funky field of four midwickets, three covers, a man under the helmet on the offside and a slip, things came alive with stomachs full.
Hampshire lost five wickets for 45 runs, in a 103 for six session.
Gubbins fell shortly after lunch for 119 when he yorked himself to a Danny Briggs delivery which then spun out the footholds. A James Fuller experiment to try and boost the run-rate failed as he swished to short third for a nine-ball five.
Amongst the drama, Middleton, a naturally shy man, looked relieved more than ecstatic to reach three figures with a cover drive, and almost needed coaxing into celebrating by proud captain James Vince.
It was a fleeting happy moment for Hampshire before Vince was adjudged caught behind and Tom Prest edged Hassan Ali to second slip - no mean feat on a pitch offering next to no carry for the seamers.
At this point the scorecard looked a curious mix of four single-figure scores and two centuries but Liam Dawson and Ben Brown made things look slightly better with a 41-run stand.
However, Hampshire's slowness meant they only picked up a single batting bonus point - inexplicable as Utilita Bowl pitches have been partly designed this season to boost that aspect which would underpin a hopeful title tilt. For comparison, Warwickshire reached their first batting point in 67.2 overs, Hampshire in 93.4.
Yates then took over to have Middleton caught bat-pad, before Dawson and Ian Holland turned him to leg slip.
The part-time spinner completed back-to-back four-wicket hauls when Kyle Abbott thumped to midwicket before Briggs wrapped things up when Ben Brown's leading edge saw him exit for 49. Hampshire were bowled out for 365, before the visitors got through 15 overs to close unharmed.