Our access in our worship is said to be "to the Father;" and this "through Christ," or his mediation; "by the Spirit," or his assistance. Here is a distinction of the persons, as to their operations, but not as their being or object of worship. For the Son and the Holy Ghost are no less worshipped in our access to God than the Father himself; only, the grace of the Father, which we obtain by the mediation of the Son and the assistance of the Spirit, is what we draw nigh to God for. So that when, by the distinct dispensation of the Trinity, and every person, we are led to worship (that is, to act faith on or invocate) any person, we do herein worship the whole Trinity and every person, by what name soever, of the Father, Son or Holy Ghost, we invocate him. (p. 269)
In worshipping or praying to the Father, we are also worshipping and praying to the Son and the Holy Spirit, for the Son and Spirit are one being with the Father. Reflect also on the great trinitarian benediction in 2 Corinthians 13:14. 'Grace' is appropriated to the Lord Jesus Christ, 'love' to God [the Father] and 'fellowship' to the Holy Spirit. But grace is also the grace of God (Romans 5:15) and of the Spirit (Hebrews 10:29). God's love is commended to us in the death of his Son and poured into our hearts by the Spirit (Romans 5:8, 5). Fellowship with the Spirit is also fellowship with the Father and his Son Jesus Christ (1 John 1:3). With that in mind, it is no more problematic to offer worship to the Holy Spirit, or pray to him, than it is to worship and pray to the Father, or the Son.
Indeed, Owen goes on to argue that we should offer distinct praise to the Holy Spirit for his work in our lives, as we rightly give glory to the Son for redeeming us by his blood, Revelation 1:5-6. We should also pray to the Holy Spirit "for the carrying on the work of our consolation, which he hath undertaken, lies our communion with him. John prays for grace and peace from the seven Spirits that are before the throne, or the Holy Ghost, whose operations are perfect and complete." (p. 271). Owen gives directions on how the believer may do just that in the following pages.
Theologically speaking then, prayer to the Holy Spirit is part and parcel of our communion with the triune God. But I promised you a proof text. Let me take you to Ezekiel's vison of the valley of dry bones. When Ezekiel prophesied to the bones they came together and were covered with flesh, but there was no life in them (Ezekiel 37:7-8). Then the Lord told Ezekiel to speak to the breath that the slain may live. The breath came and raised them to life, 'an exceedingly great army' Ezekiel 37:9-10. The 'breath' or roach in Hebrew is none other than the Spirt of the Lord, Ezekiel 37:14, compare Psalm 33:6. Israel's national 'resurrection' after the Babylonian Captivity is a picture of the resurrection of believers by the power of the Spirit, Romans 8:11. If Ezekiel could speak to the 'Spirit of life' (Romans 8:2, 10), so may we. Besides, as Owen points out, in Revelation 1:5-6, the Spirit is invoked as the source of grace and peace alongside 'him who is and who was and who is to come' [the Father] and Jesus Christ.
While the usual order in prayer is to the Father, in the name of the Son and by the Spirit, this is not a stereotypical formula in Holy Scripture. We may also call upon the name of the Lord Jesus Christ and seek the aid of the Holy Spirit in prayer.
Rest Thou upon us while we meet to pray;
Show us the Savior, all His love revealing,
Lead us to Him, the Life, the Truth, the Way.