Praying with non-Christians as evangelism? From Christianity Today, 07/02/02:


  Twelve days after the September 11 attacks, David Benke followed Catholic, Jewish, Muslim, and Hindu clerics to the podium of a Yankee Stadium event to honor the missing and the dead. Benke asked attendees to join hands and pray with him "on this field of dreams turned into God's house of prayer." He prayed "in the precious name of Jesus" and sat down.
  That prayer has led to Benke's suspension from the clergy roster of the Lutheran Church—Missouri Synod (LCMS). It has also exposed deep divisions in the church. 


Arguments I remember for this event at the time ranged from "we were overcome by events" to viewing it as an effective form of evangelism. Pr. Benke intentionally entered an arena with non-Christians and then asked them to close their eyes as he said an authentically Christian prayer.

Q: Do any events in the Bible, early church fathers, tent revivalists, or Billy Graham ,  have essentially the same features? Specifically, initiating a prayer with someone who is (not yet, not necessarily intending to become) a Christian? Perhaps the evangelism of the Apostles in either Jewish temples or public square? Did Billy Graham ever ask for public prayer at the beginning of a Crusade, before an altar call?
Prayer has never been and never will be an act only reserved for Christians. It takes its form in almost every religious belief system on the earth. 

While prayer is not unique to a religion or restricted, the problems arise with people misunderstanding prayers on behalf of others. (ie. Pr. Benke) In his specific religious sect he was praying not just for himself but for all the people in the stadium therefore speaking in the name of Christ for people who possibly did not believe. 

Theologically and scripturally there is nothing strictly against this specific act, but as we are aware religious sects interpret scripture and meaning differently.

In this case you have people who are most likely looking at prayer as an earned rite for the believers. 

For more specifics I would hope someone of that particular sect of christianity may help. But there is not canonical scriptural evidence backing the aforementioned actions in plain understanding of the text.