New Zealand claimed an encouraging 92-run victory over Essex in their tour match at Chelmsford on Monday.
Essex were bowled out for just 200 on the final day after resuming on 45-1, Michael Mason and Ian O'Brien taking three wickets apiece in the absence of skipper Dan Vettori.
England batsman Alastair Cook and Tom Westley resumed the chase but the burden soon rested with the left-hander as wickets start to tumble at the other end.
Westley drove Mills aerially to cover, and then Ravi Bopara and captain Mark Pettini went within an over of one another for the addition of a single run.
Bopara was unlucky to edge an innocuous delivery from Jacob Oram down the leg-side, and Pettini fell for the second time in the match to a very good inswinger - this one from Mason, beating a forward push to bowl him through the gate.
Cook survived a run out and a big caught-behind appeal as he made his leisurely way past 50, reaching the milestone in 114 balls with a sumptuous drive off Mason.
His innings never came close to fluency, however, and ended disappointingly on 57 with a tame drive at Mason (three for 36) into the hands of mid-off, virtually ending his side's hopes of victory.
James Foster went second ball as Essex slumped to 100-6 before Ryan ten Doeschate (38) and James Middlebrook (28) combined for a half-century stand to restore some respectability to the innings.
But O'Brien saved a good one for Middlebrook which came back between bat and pad to clip the top of middle and leg-stump, and ten Doeschate skied a catch to Brendon McCullum when his slog off part-time spinner Aaron Redmond went awry.
Alex Tudor hit a couple of boundaries but by then it was a matter of if, not when, the Kiwis would wrap up the win.