The visitors, a shade over-cautious after being in front for much of the match, did not risk a declaration until inviting the county champions to make 352 off 68 overs.
Jeetan Patel’s off-spin was a constant danger but pace was generally ineffective at the other end and the teams called it a day with Yorkshire 221 for four with four overs remaining.
Warwickshire were in a strong position at the start of the final day when they stood on 108 for two with an overall lead of 240 but there was never any indication that they would rush to a declaration.
Even when wintry showers brought forward the lunch interval by half an hour they still did not feel that a lead of 302 was sufficient.
Ian Westwood, 48 overnight, soon completed his 50 and he calmly battled on, moving ever closer to what would have been a remarkable achievement.
Had he added another century to the 196 he accumulated in the first innings, he would have become the first batsman to score a century in each innings of any first-class match on the Test ground.
But Westwood’s chance of a unique place in Headingley’s hall of fame ended on 84 when he perished lbw to off-spinner James Middlebrook, for the second time in the game after facing 134 balls and hitting 11 fours and a six.
Middlebrook continued to cash in whenever an assault was launched and he finished with five for 82 and match figures of eight for 178, a commendable effort for a player brought back to his native county specifically to fill in while Adil Rashid is in the Caribbean.
If the declaration at 219 for seven was hardly generous, it did not stop Yorkshire from attempting a positive start and Alex Lees and Will Rhodes put on 48 inside 13 overs before Lees was caught behind by Peter McKay off Rikki Clarke.
Yorkshire’s top order continued to get set and then get out, Rhodes and Cheteshwar Pujara departing lbw to Patel who turned the screw further by beating Andrew Gale with an excellent ball which found the edge for McKay to pouch again.
Patel’s three wickets placed Yorkshire under real pressure at 136 for four with 32 overs remaining and, although Jack Leaning (35no) and Andy Hodd (54no) prevented a slide, the situation would have worsened again if Varun Chopra had held on at short leg when Leaning pushed at Patel in the 48th over.
Now it was simply a case of sensible application and holding one’s nerve, which both batsmen managed despite Patel crowding the bat in the cool evening sunshine, Hodd just having time to register his 50 from 92 balls with six fours.