Mendis smashed a career-best 143 off 128 balls and Fernando made 100 off 115 in Sri Lanka's imposing total of 5-324 in 49.2 overs before rain came and reduced New Zealand's target to 221 off 27 overs.
Will Young and Tim Robinson, one of the three New Zealand debutants, combined in an 88-run opening stand but Sri Lanka derailed the Black Caps' chase through its spinners and restricted the reply to a total of 9-175.
Slow bowlers Maheesh Theekshana (2-32), captain Charith Asalanka (2-15), and Jeffrey Vandersay (1-40), in place of injured Wanindu Hasaranga, all left their mark before left-arm fast bowler Dilshan Madushanka grabbed 3-39 to give Sri Lanka a 1-0 lead in the three-match series.
Earlier, Mendis and Fernando combined in a 206-run second-wicket stand after debutant Nathan Smith took a well judged running catch at third man to dismiss Pathum Nissanka (12) in Jacob Duffy's second over after Asalanka won the toss and elected to bat.
Duffy could not hold onto a sharp low return catch from Mendis when the batter was on 11 in the only chance the pair gave before raising Sri Lanka's highest second-wicket stand in a one-day international against New Zealand.
Mitchell Santner returned 0-53 in his 10 overs while Ish Sodhi (1-62) and Michael Bracewell (1-73) were also expensive as both batters swept the spinners with ease.
New Zealand's top-order slipped against the spinners despite Young (48) and Robinson (35) combining in a decent start of 88 off 80 balls. The visitors lost five wickets for 22 runs — going from 0-88 to 5-110 — after Theekshana removed both openers in one over.
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