Sri Lanka reached their modest target with 29 balls to spare.
Man-of-the-match Chaminda Vaas dismissed captain Stephen Fleming and Ross Taylor for ducks and Muttiah Muralitharan took three for 32 to move equal top on the wicket-takers' table with 15 alongside Malinga and Australia's Glenn McGrath.
Sanath Jayasuriya (64) and Kumar Sangakkara (69 not out) shared a second-wicket partnership of 100, stroking the ball comfortably around the field with wristy cuts, pushes and drives.
Left-arm spinner Daniel Vettori took two for 35 to become the third New Zealander to capture 200 one-day international wickets.
After coming to the crease with New Zealand reeling at four for two, Styris took 20 balls to get off the mark, opening his account by driving Vaas off the back foot to the cover boundary.
He lofted Farveez Maharoof for a boundary then cut the next ball for four.
He lost Peter Fulton with the score on 71, caught by Chamara Silva off Vaas for 28. Silva took his second catch when Craig McMillan (1) top-edged a sweep off Muralitharan.
Styris scored his fourth half-century of the tournament from 82 balls with six fours and set about restoring the innings in partnership with Jacob Oram (31).
They took the total to 141 when Oram decided it was time to take control.
He hit Tillakaratne Dilshan for a six over long-on, the first boundary for 19 overs, but was well held by Maharoof trying for a repeat off the next ball.
James Franklin (25 not out) and Styris shared a bright unbeaten eighth-wicket partnership of 64 from 9.1 overs to take their team past the 200 mark.
Styris reached his second World Cup century from 152 balls with a pull shot for four and the pair took 17 off the 50th over bowled by Vaas.
The Sri Lankans got away to a flying start helped by three dropped catches.
Fleming floored Upul Tharanga on eight and McMillan spilled Jayasuriya on 30.
McMillan, at mid-on, got his fingertips only to a chance from Sangakkara when the Sri Lankan wicketkeeper had made nine.
Tharanga made only three more runs before he was caught on the third-man boundary by Shane Bond off Franklin.
Jayasuriya greeted Mark Gillespie's first ball of the tournament by hooking it for six and the second for four.
The over cost 17 runs.
He brought up his 63rd one-day international half-century from 65 balls with three fours and a six, falling finally when he was caught behind off Oram by Brendon McCullum standing up to the stumps.
Sangakkara completed his 39th one-day century from 56 balls with one boundary and ended the match with a four off Gillespie.
The seven-week World Cup culminates with the April 28 in Barbados.