An own goal from Nigerian midfielder Oghenekaro Etebo gave Croatia a half-time lead in Russia, before Luka Modric secured all three points with a second-half penalty to cap off an efficient performance against a lacklustre Super Eagles.
A turgid opening saw both sides sizing each other up for most of the early stages, and it took the best part of 14 minutes for Croatia to create something in front of goal.
When it came, however, the build-up play was incisive as Modric drove in off the left flank to find the feet of Ante Rebic. The youngster set the ball dead on the edge of the area for Ivan Perisic, who saw his bending effort creep just over Francis Uzoho's crossbar.
Nigeria's side, the youngest on average at the tournament, sat deep for much of the first period as Croatia took possessional control of the encounter.
Dalic's side created little of note before the break but Croatia somehow took a fortunate lead when Mario Mandzukic found himself on the end of a corner, leaving his resulting header to cannon into Etebo and past Uzoho in the 32nd minute.
With little forward-moving resistance coming from Nigeria, Modric sought to make use of the space on the edge of the box ahead of the interval, crossing acutely for Andrej Kramaric, who saw his deft header loop just over the bar.
Nigeria were slightly improved in the second period and it took some clever defending from Perisic to thwart a header from Leon Balogun, who had arrived late at the front post to meet a Victor Moses corner.
Croatia showed little interest in securing a two-goal advantage after the break, although a piece of standout quality from the left foot of Perisic laid a goal on a plate for Rebic, only for the forward to somehow guide his half-volley over the bar from close range.
A lack of Croatian ambition in the final third might have left Nigeria with a route back into the game, but that door was soon closed in the 69th minute when centre-back William Troost-Ekong conceded a penalty having unnecessarily grappled Mandzukic inside the box.
The foul, committed right under the nose of referee Ricci Sandro, gave Modric the chance to double the Croatians' lead from the spot.
The Real Madrid midfielder made no mistake as he sent Uzoho the wrong way to make it 2-0 and confirm all three points from a rather forgettable contest in the Russian exclave of Kaliningrad.
CROATIA (4-2-3-1): Subasic; Vrsaljko, Strinic, Lovren, Vida; Rakitic, Modric; Perisic, Kramaric (Brozovic 60'), Rebic (Kovacic 78'); Mandzukic (Pjaca 86')
NIGERIA (4-2-3-1): Uzoho; Abdullahi, Ekong, Balogun, Idowu; Etebo, Ndidi; Mikel (Simy 88'), Iwobi (Musa 62'), Moses; Ighalo (Iheanacho 73')