Necid struck after 29 minutes at the Toumbas Stadium with the away goal making the Russian side favourites to progress ahead of the return leg in Moscow next week.
With the Russian domestic season ending in November, CSKA had not played a match since drawing with Sparta Prague in their final Europa League group game on December 15.
And their rustiness was apparent as Bruno Cirillo was allowed an early shot for PAOK before Vieirinha's curling free-kick had to be punched clear by Igor Akinfeev.
The CSKA goalkeeper did even better after 12 minutes, tipping a first-time shot from Dimitris Salpingidis round the post, before Vladimir Ivic headed the resulting corner over the target from close range.
CSKA had to wait 22 minutes for their first chance, although it was a speculative shot from distance by Aleksandrs Cauna which cleared the crossbar.
The visitors soon began to grow in confidence, though, and Zoran Tosic came much closer with a left-footed strike which curled just past the left upright.
And they were in front after 29 minutes thanks to Necid, who neatly tucked away a cross from Georgi Shchennikov into the bottom right corner.
Having got themselves on the scoreboard, CSKA looked to add to their lead and PAOK goalkeeper Kostas Chalkias had to be at his best before the interval to keep out efforts from Seydou Doumbia, Necid and Tosic.
Chalkias failed to emerge after the break due to injury, with Dario Kresic taking his place between the posts.
Lino then tried to produce an equaliser for PAOK but could only aim his free-kick straight at Akinfeev.
Kresic saw his first action after 53 minutes holding onto a free-kick from Tosic, and caused further frustration for CSKA 10 minutes later with two fine saves in quick succession to palm away shots from Tosic and Pavel Mamaev.
Both sides continued to have their chances as the half wore on, Stavros Tsoukalas driving wide for PAOK before Necid also directed an effort past the right post.
Substitute Nabil El Zhar had one final chance to equalise for the Greek hosts seven minutes from time, but Akinfeev was equal to the challenge, punching away his 18-yard drive.
PAOK Salonika 0-1 CSKA Moscow: Match Report - view commentary, squad, and statictics of the game as it happened.
Source: DSG
