“We felt like we left a few shots out there but we were just saying the two foursomes days on Friday and Sunday here are the important days in this tournament,” added McIlroy, 35.
“It’s important for us to obviously post a good score tomorrow.”
Collin Morikawa and fellow US player Kurt Kitayama are in the group sharing third place after a 61, with England’s Matt Wallace and Danish partner Thorbjorn Olesen a further stroke back.
England’s Aaron Rai and American Sahith Theegala shot a 63 with the pairings of Scotland’s Robert MacIntyre and Belgium’s Thomas Detry and European Ryder Cup captain Luke Donald and Colombia’s Camilo Villegas sharing 28th spot with McIlroy and Lowry.
The fourball element sees both players hitting their own ball with the best score counting, while players take alternate shots with one ball in the foursomes.
The reigning champions have never successfully defended the Zurich Classic title.