At stumps on the second day of the four-day contest, Zimbabwe XI, who were shot out for a paltry 94 in the first innings, showed better application in their second essay to be 50 for one in 21 overs.
They need another 214 runs to make North Zone bat again.
Earlier, North openers Ricky and Dhawan resumed at 62 without loss and put on a double century stand.
Dhawan made 117 in 283 minutes and hit 18 fours before he was sent back by off-spinner Prosper Utseya who ended up with three wickets.
Manvinder Bisla was dismissed cheaply, the first of seven victims claimed by leg spinner Graeme Cremer.
Then Ricky, who made 106, also fell to the Zimbabwe leggie to trigger a procession of batsmen to the pavilion.
The middle order collapsed against the double spin attack of Cremer and Utseya, barring Yashpal Singh, who remained unbeaten on 51, with three fours and a six.
Yashpal also put on 72 runs for the last wicket with his captain Amit Bhandari who made 22 before spooning a skier to Cremer off the leggie's own bowling.
Cremer finished with fine figures of seven for 114 while Utseya, who played against India in the Test series back home, grabbed three for 78.
Trailing by a huge first innings margin, Zimbabwe lost opener Neil Ferreira to off-spinner Sarandeep Singh but Terence Duffin and Vusi Sibanda prevented any further loss.