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The hosts never allowed New Zealand to build a big partnership in the day-night match, with fast bowlers Malinga taking 3-35 and Mathews 3-36.
The highest stand of the innings was 52 for the fourth wicket between opener Watling (55) and all-rounder Scott Styris (24). Nathan McCullum was the other notable contributor with 36.
Malinga struck with the second delivery of the match when he had Martin Guptill caught by Chamara Kapugedara for his 100th victim in one-day internationals.
Watling and skipper Ross Taylor (16) then put on 45 runs for the third wicket before Mathews bagged two wickets off three balls to reduce the visitors to 47-3.
Mathews trapped the New Zealand captain leg-before and then had Kane Williamson caught by Thilan Samaraweera in the slips for a second successive duck.
Watling, 25, completed his half-century in style when he hit left-arm spinner Rangana Herath for a four. He fell soon, top-edging a pull off Mathews to be caught by wicket-keeper Kumar Sangakkara.
He struck eight fours in his 68-ball knock.
Malinga grabbed two wickets off successive balls in his second spell, dismissing Gareth Hopkins (11) and Daryl Tuffey for no score.
New Zealand made three changes from the side that thrashed India by 200 runs in the opening match on Tuesday, bringing in Watling, McCullum and Tim Southee in place of Peter Ingram, Jacob Oram and Grant Elliott.
Each side will play the other twice in the preliminary league before the top two qualify for the final on August 28.
New Zealand
BJ. Watling c Sangakkara b Mathews 55
M. Guptill c Kapugedera b Malinga 0
R. Taylor lbw b Mathews 16
K. Williamson c Samaraweera b Mathews 0
S. Styris c Jayawardene b Herath 24
G. Hopkins c Kapugedera b Malinga 11
N. McCullum c Herath b Mendis 36
D. Tuffey b Malinga 0
K. Mills c Mathews b Herath 11
T. Southee c Dilshan b Kulasekara 13
A. McKay not out 4
Extras (b5, lb4, nb3, w10) 22
Total (for all out; 48.1 overs) 192
Fall of wickets: 1-2 (Guptill), 2-47 (Taylor), 3-47 (Williamson), 4-99 (Styris), 5-101 (Watling), 6-123 (Hopkins), 7-123 (Tuffey), 8-143 (Mills), 9-178 (McCullum), 10-192 (Southee)
Bowling: Malinga 10-1-35-3 (nb3, w4), Kulasekara 8.1-1-35-1 (w1), Mathews 10-1-36-3 (w1), Mendis 10-0-42-1 (w4), Herath 10-0-35-2
Umpires: Kumar Dharmasena (SRI) and Simon Taufel (AUS)
TV umpire: Tyron Wijewardene (SRI)
Match referee: Alan Hurst (AUS)
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