Lancashire began day four on 264 for six and have advanced to lunch at 395 for eight, a deficit of 53.
Azeem Rafiq struck twice as he had Stephen Parry caught at short-leg and Ryan McLaren caught behind reverse sweeping.
Parry and McLaren shared 70 for the seventh wicket to take the hosts beyond the follow-on target of 299.
Parry hit 39 and McLaren 84, falling short of only his second career century in county cricket, as the hosts fell to 344 for eight.
Tom Bailey and Simon Kerrigan have since shared 51 unbroken for the ninth wicket. Bailey has 39 not out and Kerrigan 31.
Despite Yorkshire being on top for much of this match, Lancashire will end it with 10 points to Yorkshire’s nine assuming a draw is confirmed later today.