Coad, who lodged his maiden first-class five-wicket haul in defeat at home to Hampshire last week and followed up with another in the first innings in Birmingham, added a third with 5-27 – giving him 10-79 in the match.
It left the home side’s batting line-up in tatters, with Warwickshire, requiring 203 to avoid an innings defeat, eventually ending the third day on 85-9.
Yorkshire were denied the opportunity to wrap up victory inside three days due to the fading light that forced the teams off at around 7.15pm.
Coad fed voraciously on Warwickshire’s brittle confidence and, as if his match could not get any better, his victims included Warwickshire captain and former England batsman Ian Bell.
Following his first-innings haul, the 23-year-old admitted the Warwickshire wickets he coveted most were Bell and Jonathan Trott.
After dismissing the latter in the first innings, he removed Bell in the second with a brute of a ball, which lifted to take the glove on its way to slip.
At one stage, Warwickshire were 7-5 and by no means certain to reach 35, their lowest total against Yorkshire. They avoided that embarrassment but their collapse was alarming enough.
Afterwards, Yorkshire captain Ballance was quick to praise his team’s efforts, although he understandably singled out Coad, who has been a revelation for the White Rose after coming in to fill the gap left by injuries to the club’s leading pace bowlers, including Ryan Sidebottom, Liam Plunkett and Jack Brooks.
“This morning the guys batted very well to get us a lead of just over 200, which was perfect,” said Ballance.
“We put a lot of pressure on them. Then, the way the guys bowled, Dave and Coady set it up brilliantly. They bowled very well and took some early wickets.
“Last week, we played some good cricket for most of the game. We were disappointed to lose, but we came into this game with a bit of confidence, and so far the guys have proved it.
“I’ve seen Ben bowl for the last two months, and I knew that he could bowl well and put in good performances. But, honestly, I can’t say I would have seen him doing this well.
“It’s brilliant bowling and he’s done it by getting top players out. It’s deserved. The hard work he’s put in is paying off now.
“He must be surprised. He’s got 18 wickets in four innings. I think anyone would be surprised. You don’t expect someone to come in for their second championship game and tear it up like he is. He’s done very well and, hopefully, he can carry on.
“We’ve played some good cricket in this game, and we’ve been a bit more ruthless than we were last week against Hampshire, which is what we spoke about.”
After Yorkshire resumed on 295-6, Adil Rashid and Andrew Hodd extended their partnership to 52 before the latter was bowled by Keith Barker.
Rashid reached his 37th first-class fifty, but then edged Rikki Clarke to Trott at slip for an innings of 65 that included 10 fours during his 96-ball stay.
Trott pounced again to catch Steve Patterson off Clarke and David Willey nicked Olly Hannon-Dalby but, with the lead past 200, Yorkshire’s pacemen were keen to get bowling.
Warwickshire were then blitzed by a devastating passage of play.
In six overs between lunch and a rain-break they scored one run and lost three wickets.
Willey’s fifth ball after lunch removed Alex Mellor, caught by Tim Bresnan at first slip, and his sixth pinned Trott lbw.
Bell kept out the hat-trick ball, but collected only a single before copping a near-unplayable offering from Coad.
After rain lopped off 21 overs, Coad resumed his rampage.
He knocked out Sam Hain’s off-stump as the batsman offered no shot, trapped Tim Ambrose lbw and had Rikki Clarke caught at second slip.
Further rain after tea, with Warwickshire 36-6, cleared to leave Yorkshire 11 overs to try to finish the match off in three days.
Patterson had Barker caught behind, William Porterfield edged Coad into the cordon and Rashid bowled Wright.
But, frustratingly, the light closed back in before the 10th wicket could be captured.
On Saturday, Australian Test star Peter Handscomb showed exactly the quality that Yorkshire hoped he would inject.
In reply to the home side’s 178, Yorkshire finished the day 117 ahead, and it was Handscomb who caught the eye.
Coming in at 9-1 after the early dismissal of Adam Lyth, the 25-year-old batted with immediate freedom and confidence. He enjoyed some luck, especially early on, but seized rapaciously on anything loose on his way to 75 off 110 balls, including 12 fours.