The Colombia midfielder beat Igor Akinfeev from the edge of the box to give the Portuguese Liga leaders the advantage heading into the last-16 second leg.
It was a fair enough result after Porto shaded the best of what chances there were, though both sides were in the main reduced to shooting from distance.
Falcao tested Akinfeev after five minutes, the CSKA goalkeeper punching clear his shot from 18 yards.
Guarin was next to try his luck moments later but his strike from distance was held by Akinfeev.
Joao Moutinho and James Rodriguez also sent in shots from outside the box before 10 minutes were up, but neither could test Akinfeev.
After that the balance shifted with play moving largely down the other end.
Helton held onto Vagner Love's shot from 12 yards in the 13th minute, then fisted away an 18-yard strike from the Brazilian.
Their personal battle resumed in the 23rd minute with the goalkeeper punching clear another effort, before Kirill Nababkin fired Keisuke Honda's cross over the bar, but it was Porto who finished the half stronger.
Akinfeev caught Falcao's free-kick and beat away Guarin's long-range effort, while Cristian Sapunaru's shot was wayward.
It was more of the same after the break with plenty of shots raining in, but few from really dangerous areas.
Joao Moutinho and Hulk both tried their luck but failed really to stretch Akinfeev.
As Porto pressed the chances started to get better and Sapunaru headed Hulk's free-kick over the bar from 12 yards after 66 minutes.
If either side was going to score, Porto seemed the more likely and so it proved as Guarin beat Akinfeev with a low strike from the edge of the box.
That spurred CSKA into life, with Pavel Mamaev and Vagner Love both firing wide.
Helton was called into action from Seydou Doumbia's shot, but he held on - and so did Porto.
CSKA Moscow 0-1 FC Porto: Match Report - view commentary, squad, and statictics of the game as it happened.
Source: DSG
