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Warwickshire 244 (Burgess 96) and 252 for 3 (Rhodes, 111, Hain 109) drew with Yorkshire 449 (Lyth 145, Brook 82, Revis 53*)
Champions Warwickshire started day four on 57 for three in their second innings, a deficit of 148, and when the players shook hands at 4.50pm they were 252 for three with a lead of 47.
Hain and his captain Rhodes, a Championship winner with both of these counties, shared 227 inside 104 overs for the fourth wicket and finished on respective personal scores of 109 and 111.
This was a game which unbeaten Yorkshire had much the better of, but they had to settle for a fifth draw in six Division One matches this season. They took 14 points to Warwickshire's 11.
In four of their five draws, Yorkshire have had final-day victory chances both at home and away only to be thwarted by a mixture of determined batting in benign conditions and without the bowling firepower they would have wanted.
That was exactly the case here as the champions, against an attack minus quicks Matthew Fisher, Ben Coad and Haris Rauf through injury or illness, added their fourth draw to a win and a defeat.
Heading into the break for the start of the Vitality Blast, Yorkshire have gone third in the table, 15 points behind leaders Surrey (105), while Warwickshire remain sixth.
Hain and Rhodes batted through a quiet morning session with only a couple of obvious alarms and brought up their centuries off successive balls shortly after tea.
They batted with more purpose than they had done late on day three having come together at 25 for three following Jordan Thompson's trio of new-ball successes.
A Rhodes edge off Dom Bess flashed through Harry Brook at second slip before he had chance to react and Hain edged the same bowler in between his off stump and wicketkeeper Harry Duke to reach his fifty off 188 balls.
Seventy one runs came in the morning as the score advanced to 128 for three at lunch, with a minimum of 64 overs remaining.
Yorkshire's best hope was a new ball due seven overs into the afternoon, going some way to explain why they bowled double spin in the form of Bess and Joe Root either side of lunch.
They took it with 57 overs remaining, when Warwickshire were 146 for three and still 59 behind.
The pitch had shown signs of offering turn and had been a bit two-paced during day three, but there was none of that 24 hours later.
Hain was particularly punishing on the cut shot, which brought him a solitary six off Matthew Revis. Rhodes was stronger to leg, both working through midwicket and pulling with authority.
When Warwickshire reached tea at 222 for three, they led by 17 with a minimum of 34 overs remaining with Rhodes on 98 and Hain unbeaten on 92.
During the afternoon, Rhodes had edged Steve Patterson short of Root at slip. Immediately the former England captain left the field, only to return to field in the same position with his right thumb strapped.
Rhodes and Hain reached their centuries in the early stages of the evening, by which stage they had only just recorded a double century partnership.
Hain's second hundred of the season came off 308 balls and a first of 2022 for Rhodes came off 268. Warwickshire were 232 for three, leading by 27 with almost 30 overs remaining. The job was complete.
It has been an inconsistent start to the season for Warwickshire, though rearguard this will give them great heart.
Under the guise of the Birmingham Bears, they start their Vitality Blast campaign against Northamptonshire at Edgbaston on Thursday evening.
Twenty four hours earlier, Yorkshire host Worcestershire at Headingley.
Will Rhodes, Sam Hain centuries guide Warwickshire to battling draw against Yorkshire
Hosts unable to build on Thompson's three early strikes thanks to doughty 227-run stand
Jordan Thompson's new-ball burst prompts Warwickshire shiver of realisation
Defending champions respond grudgingly after realising their standing is in doubt
Harry Brook, Adam Lyth find blend of virtues to keep Yorkshire thriving in spite of everything
Cheap dismissal of Joe Root can't dent progress, as young-old partnership holds firm