Worcestershire 415 for 8 (Mitchell 113, Barnard 98*, Haynes 65) lead Warwickshire 395 (Malan 141, Sibley 80, Rhodes 60, Sodhi 6-89) by 20 runs
Warwickshire are on the brink of sealing a top two spot in Group 1 of the LV= Insurance County Championship despite encountering prolonged Worcestershire resistance in the New Road derby.
But the Bears will seal a spot amongst the six teams who will fight it out for the Championship crown in September if they avoid defeat on what is still a flat pitch in a game where only 18 wickets have so far fallen.
Mitchell's ton was the 39th of his career while Barnard fully justified his promotion into the top six.
Worcestershire resumed on 152 for 2 and Haynes soon brought up a half-century from 110 balls with six fours in his first senior innings since a five week lay-off with an ankle problem.
The 100 stand with Mitchell occupied 264 balls and the veteran opener completed his hundred with a single off Will Rhodes.
It came from 228 balls with 10 boundaries and Mitchell has moved into the top six of Worcestershire's all-time century-makers.
Matt Lamb made the first breakthrough of the day when Jack Haynes (65) was caught off a leading edge at extra cover to end a stand of 130 with Mitchell.
Mitchell's fine knock ended 11 runs later on 113 when he played forward to Liam Norwell and was lbw.
Warwickshire continued to chip away and captain Will Rhodes struck in successive overs as Brett D'Oliveira (18) was caught behind and Ben Cox (1) checked his shot and offered a return catch.
Worcestershire Club Captain, Joe Leach, produced some aggressive batting and collected three boundaries in an over from Rhodes.
He made a quickfire 34 before he was caught down the legside off Rob Yates.
Barnard, promoted after impressive early season form, batted responsibly and swept Yates for four to bring up the 300.
Ish Sodhi (13) picked out deep mid wicket off Lamb but Barnard completed a 122-ball fifty with his fifth four.
Adam Finch helped him add a further unbroken 91 for the ninth wicket. Barnard needed three from the final over to reach his hundred but was content to take a single off the second ball. He hit eight fours in his 195-ball knock.