Ben Coad returned a brilliant 3-44 from 21 overs, well backed up by three wickets for new ball partner Matthew Fisher as Yorkshire gained a first-innings lead of 63, the hosts bowled out for 263 in reply to 326.
Coad and Fisher led an eight-man attack who ramped up the pressure on a Gloucestershire line-up determined to dig in on a placid pitch and take time out of the game.
Australian opener Cameron Bancroft’s 70 off 196 balls with three fours epitomised that, as did the hosts only scoring one boundary in the morning as they advanced from 28-2 to 88-3.
That pressure told, as Glos slipped from 126-3 after lunch, with Coad striking twice in an over with the new ball.
Adam Lyth and Fin Bean then closed the day on 57-0 from 11 overs, ensuring an overall lead of 120 with two days remaining.
Coad said at close: “I’m very happy.
“It did enough with the new ball, but it’s quite a slow pitch. If you bowl in the right areas, it’s hard to score but quite tricky to take wickets. So I think we’ve done a great job there.
“The way they batted, they’ve tried to grind us into the dirt. But we’ve held onto our lines and lengths immaculately.
“It was very dry and they weren’t doing a lot. We just had to stay patient.
“We knew the new ball was around, so we knew a few wickets and we’d be into them. Then we struck with the new ball again.
“It’s very much a new ball pitch, so the way Lythy and Bean have batted, it’s perfect for setting us up.”
Yorkshire have done very well to engineer a position of significant strength having been 90-5 at lunch on day one having been invited to bat first.
“It was a big toss to win,” said Coad. “They were perfect conditions to bowl first in.
“The way Shan, Tatts, Milnesy batted was a great effort to put us in a good position.
“We knew we had a good score, and bowling well would put us in a good position. That’s what we’ve done.”
Whisper it quietly, but there has been a suggestion that there is rain around in Bristol on Monday. So will that affect Yorkshire’s thinking with the bat tomorrow. Will they push on to declare a bit earlier?
“We’ve got the players to do it,” added Coad.
“I haven’t looked that far ahead, but I’m sure tomorrow we’ll have a look.
“We have the players to push on, so if we’re in a position to pull out early then I’m sure we will do. We’ll always try and win the game.”