The visitors were all out for 194, 210 behind, and in four overs' batting Durham reached 16 without loss in their second innings after opting not to enforce the follow-on.
Yorkshire would have been in much deeper trouble but for a plucky innings of 70 by Adil Rashid, who rescued them from 50 for six in a stand of 85 with Tim Bresnan.
Steve Harmison took two early wickets and added a third when Rashid was last out, going for a big swing and edging to wicketkeeper Phil Mustard after hitting 11 fours in his 121-ball knock.
Harmison was nowhere near as accurate as Onions, who twice went agonisingly close to bowling Jacques Rudolph during a 12-over opening spell in which his three wickets were fully deserved.
He returned to bowl Bresnan for 46, which included eight fours after the pressure was eased when Onions made way for Ben Harmison's medium pace.
Onions then trimmed Darren Gough's off bail to finish with excellent figures of five for 75 from 20 overs, while Harmison senior had three for 40.
After Yorkshire's left-handed openers, Joe Sayers and championship debutant Adam Lyth, both edged to Neil McKenzie at first slip, Anthony McGrath was brilliantly run out by substitute Will Gidman.
He was on the field for only a few overs but swooped from mid-wicket to hit the non-striker's stumps after McGrath called for the single.
Andrew Gale edged Onions to second slip and wicketkeeper Gerard Brophy looked too high at six as Onions almost bowled him and then induced an edge to Mustard.
Rudolph fenced at the first ball of the next over from Steve Harmison and gave the wicketkeeper another catch.
When Durham batted again Ben Harmison opened in place of Di Venuto, who suffered a hand injury while attempting a stop in the slips.

Durham v Yorkshire
Riverside: Durham (8pts) lead Yorkshire (3) by 228 runs with all 2nd inns wkts standing.
Durham first innings 406 (M Di Vento 184)

Yorkshire first Innings
J J Sayers c McKenzie b Onions 8
A Lyth c McKenzie b S J Harmison 7
A McGrath run out 6
J A Rudolph c Mustard b S J Harmison 5
A W Gale c Di Venuto b Onions 13
G L Brophy c Mustard b Onions 4
A U Rashid c Mustard b S J Harmison 70
T T Bresnan b Onions 46
D Gough b Onions 1
G J Kruis c McKenzie b Davies 22
B W Sanderson not out 0
Extras lb11 w1 12
Total (61.1 overs) 194
Fall: 1-16 2-20 3-29 4-42 5-50 6-50 7-135 8-139 9-194
Bowling: S J Harmison 15.1 4 40 3; Onions 20 3 75 5; Davies 13 4 23 1; B W Harmison 6 1 19 0; Wiseman 7 1 26 0.

Durham Second Innings
M D Stoneman not out 9
B W Harmison not out 6
Extras w1 1
Total 0 wkts (4 overs) 16
Bowling: Bresnan 2 0 10 0; Gough 2 0 6 0.