Messi's double in the Catalans' 2-0 win at Ajax three weeks ago took him level with Real Madrid legend Raul's record tally of 71 goals in the competition and ensured Barca's progress to the last 16 for an 11th consecutive season.
However, Luis Enrique's men still need at least a point in Cyprus to ensure they can win Group F with victory over Paris Saint-Germain at home in their final group match early next month.
Luis Suarez's attempts to break his Barcelona duck were frustrated once more but Enrique has no concerns over the Urguayan's ability to find the back of the net as he again proved his worth with a fourth assist in as many games.
"It will come. To have a goalscorer of that quality and generosity is marvellous," said Enrique.
Rakitic also hailed the importance of such a resounding win after a difficult couple of weeks which saw Barca lose to Real Madrid and Celta Vigo in consecutive games before struggling to overcome Almeria 2-1 ahead of the international break.
"It was important to play well and recover good feelings, but above all to regain the confidence of the fans."
The Croatian is likely to team up with Xavi Hernandez in midfield as Andres Iniesta has been left out of the 22-man squad that will travel to Nicosia on Monday, despite nearing a return to action after a month out.
Three narrow defeats from four matches mean APOEL cannot repeat their remarkable run to the Champions League quarter-finals in the 2011/12 season, but they too still have the prospect of European football into the new year to fight for.