One of the scriptures that guides me to pray to the Father "through" Jesus or in the name of Jesus is Matt. 18:19,20 " 'Again, I tell you that if two of you on earth agree about anything you ask for, it will be done for you by my Father in heaven. For where two or three come together in my name, there am I with them.' " --New International Version
Here is another scripture that supports the idea of praying in Jesus' name. John 14:13,14 " 'And I will do whatever you ask in my name, so that the Son may bring glory to the Father. You may ask me for anything in my name, and I will do it.' " --New International Version
The apostle Paul also supports the idea of praying in the name of Jesus at Colossions 3:17 "And whatever you do, whether in word or deed, do it all in the name of the Lord Jesus, giving thanks to God the Father through him."
For me personally, praying in the name of Jesus or through Jesus is acknowledging that he is The Way to the Father, that his role as Mediator is vital in my relationship with God.