Well, basically, Catholics commit themselves to the Sacred Tradition of the Church because it is out of this Tradition that Scripture came, because Scripture itself recommends and confirms this Tradition, and because nothing in Scripture says that this Tradition should cease to be authoritative in the lives of Christians once content from that Tradition was written down and canonized.
By "Sacred Tradition" I mean the various ways in which the teaching of the Apostles, the "deposit of faith," is passed on and preserved by the Church. This deposit was preserved and passed on through the writing of Sacred Scripture, which was inspired by the Holy Spirit, but it also was (and continues to be) preserved in the ordinary teaching of the successors of the Apostles (the bishops), in the writings of the early Church Fathers, in the authoritative documents of the Church (encyclicals, apostolic exhortations, dogmatic constitutions, conciliar canons, etc.), and in the liturgical worship of the faithful. Since the teaching and preaching of the Apostles has a divine origin, as does the consigning of that preaching to writing, both the preaching and the writing comprise the "Word of God" and thus "must be accepted and honored with equal sentiments of devotion and reverence" (Dei Verbum, no. 9).
Paul is particularly adamant about respecting this Tradition. He presents Scripture and Tradition as standing alongside each other (cf. 2 Thes 2:15; 2 Tim 3:10,14-15). He affirms the Tradition that his audience has received (cf. Rom 10:8,17; Gal 1:11-12; Eph 1:13-14; Col 1:5-7; Titus 1:3), commands them to follow it (cf. Phil 4:9; 1 Thes 4:1-2; 2 Thes 3:6-7; 2 Tim 1:13), and praises them when they do (cf. 1 Cor 11:2; 15:1,3,11; 1 Thes 2:13). There is simply no indication from his writing that he wished for them to do away with Tradition. Instead, he seems to be affirming it around every corner. There is also no indication that this Tradition would somehow cease to exist or to be authoritative. Instead, Paul indicates that it will continue forever (cf. 1 Tim 6:20; 2 Tim 2:2) [Peter does too, cf. 1 Pet 1:25; 2 Pet 1:12,15].
Note that, whenever "tradition" is condemned in Scripture, for example, by Jesus (cf. Mt 15:3-9; Mk 7: 8-13) or by Paul (cf. Col 2:8), what is being condemned are the traditions of men, or traditions that are contrary to the Word of God. The authentic, Sacred Tradition of the Church, however, has its very source in Jesus Christ and is preserved by the Holy Spirit working in the Church. Surely you can see why I would not think that those verses apply, and really, in order to prove that they do, you would have to prove that some element of the Sacred Tradition of the Church was contrary to the written articulation of it in Scripture.
I hope that answers your question. There are many different ways to articulate what Sacred Tradition is, and what the relationship is between it, Scripture, and the Magisterium (or teaching office) of the Church. I highly, highly suggest reading the Catechism, nos. 74-95, and Dei Verbum (Dogmatic Constitution on Divine Revelation, from the Second Vatican Council) in full.