CD are 211-3 in their second innings, leading by 265 runs, with Greg Hay unbeaten on 95.
Wellington had earlier declared on 370-7, 54 runs behind CD's first innings effort. Tom Blundell top scored with 92, while CD seamer Kurt Richards took three wickets in his return to domestic cricket after eight seasons away.
Elsewhere, Northern Districts are batting for survival against Canterbury at Seddon Park in Hamilton.
The hosts are 237-6 in their second innings, holding a slender lead of nine runs. Bharat Popli (71) and Scott Kuggeleijn (27) have combined for an unbroken 57-run stand, and they'll need to bat for a lengthy period on the final day to avoid defeat.
ND continue to get classy performances from Popli, who is the leading runscorer in the Plunket Shield, while Kuggeleijn has a massive lead atop the wicket-taking ladder after claiming four scalps in Canterbury's first innings.
Unwanted international spinners were also at the forefront - Ish Sodhi backing up his seven wicket display last week with 5-167, and Todd Astle bowling 27 overs unchanged for the visitors who are on track for victory.