Mitchell entered the fray when New Zealand were 39-3 after Binura Fernando had rattled the top order.
He was joined by Bracewell when Wanindu Hasaranga took two wickets in two balls to reduce New Zealand to 65-5 in the 10th over.
The pair put on 105 before both were dismissed in the final over.
Mitchell was stumped for 62 off 42 deliveries while Bracewell was caught behind for 59 off 33.
Fernando, who removed both New Zealand openers in his second over, finished with 2-22.
Tim Robinson was caught and bowled for 11 when he drove a short-pitched delivery straight back to the bowler.
Three balls later Rachin Ravindra, on eight, nicked an outswinger and was caught behind.
Mark Chapman, dropped on four, reached 15 before he was caught on the boundary by Kamindu Mendis off the bowling of Matheesha Pathirana.
Glenn Phillips had made eight off nine deliveries when he was trapped in front and Mitchell Hay went first ball when he played and missed at a ball drifting into the pads.
