After the hosts resumed on 205-2, Varun Chopra added just six to his overnight score before being caught in the slips off Steven Patterson for 107.
Jonathan Trott (74) and Tim Ambrose (61 not out) ensured full batting points for the Bears, who declared on 443-9.
The visitors lost Adam Lyth and Alex Lees cheaply as Yorkshire reached 73-2 before the players shook hands.
Yorkshire, who have started the defence of their Division One title with two draws, now face Nottinghamshire in a match which begins on Sunday.
But they will be without Ryan Sidebottom, whose ankle injury, sustained on day two at Edgbaston, will rule him out of next week's game against his former county Nottinghamshire at Trent Bridge.
Three successive draws at the start of the season have been enough to take Warwickshire to the top of the table, although they have played at least a game more than all the other Division One sides.
Warwickshire captain Ian Bell told BBC WM:
"Being top of the table at this stage of the season doesn't really mean anything but the start we have made is very encouraging.
"The challenge was to get 400, which wasn't going to be straightforward against a good attack, but we did it quite comfortably in the end.
"Tim Ambrose and Rikki Clarke batted really well in the middle order. They are important players for us. Them getting runs is a good sign because we have got big runs at the top of the order in the early games.
"But also the engine-room, from 6 down to 10, is producing well. If they are batting well too, it just keeps the pressure on the opposition."
Yorkshire captain Andrew Gale told BBC Radio Leeds:
"We know we are playing 'okay' cricket but know we can be better. We are not playing our best cricket but have still got two solid draws.
"I don't think we have hit our straps in the top five with big partnerships and we haven't bowled in partnerships either.
"There have been periods of play when we have been quite sloppy and gone round the park.
"The encouraging thing is the lads recognise that and want to work hard to put it right. While they are doing that you know you are on the right path.
Warwickshire and champions Yorkshire settled for a draw on day four of their rain-affected game at Edgbaston.