Anderson (82, 4X4s&4X6s) steered Kiwis to a competative 221/8 in stipulated 50 overs. In reply Zimbabwe crumbled and was eventually all out for 123 thanks to a fine spell from Tim Southee, who ended with figures of 5-11 off 8.4 overs.
Only Daniel Landman (51) provided any real resistance to the Southee-led Kiwi onslaught.
New Zealand will take on defending champions Pakistan in their next Group-A tie at the same venue 'morrow while Zimbabwe face hosts Malaysia in their must-win game.
New Zealand 221/8 in 50 overs ( Anderson 82, Morgan 27; Masvaure 3 for 37, Landman 2 for 42, Ncube 1 for 7) beat Zimbabwe 123 all out in 42.4 overs (Landman 51, Mire 31; Tim Southee 5 for 11, Anurag Verma 1 for 15) by 98 runs.