Pinchas' act was not only important insomuch as it stopped horrific chillul Hashem. His zealotry was also crucial in its impact on the masses who were witness to Zimri's violation. The Torah recounts the pandemonium which reigned just before Pinchas stepped in (25:6). The public idolatry at Baal Peor coupled with the heathen orgy tore everything asunder. Jewish existence was in a state of turmoil, and there was absolutely no consciousness of God's Law and Word. All commitment to Hashem was unraveled and seemed to be permanently irrelevant. Pinchas' act shocked the people back into religious reality and enabled them to reconnect to God. This is the meaning of Hashem's reward of "sholom" (ibid. v. 12), for sholom is defined as wholeness, as connection between parties. In this case, the parties were Hashem and the Jews.
It is thus understood why Pinchas is identified as Eliyahu Ha-Navi (see Targum Yonasan ben Uziel, ibid.), for Eliyahu, too, will come to a world which has lost all sense of connection to Hashem and is steeped in false ideologies and acts of desecration, and Eliyahu will restore consciousness of God and connection to Him with the herald of the coming of Moshiach.
Still, how do the importance of Pinchas' actions and his reward relate to the rest of the parshah?
Rashi and the Torah Temimah quote the Sifri regarding the commandment of the Korban Tamid (28:1). The Sifri links this mitzvah with the appointment of Yehoshua and indicates that the Korban Tamid was to serve as a preventative against straying after idolatry. The Sifri states that just as Moshe "commanded" God to provide a new leader for the Jews, so did God command Moshe (the mitzvah of the Korban Tamid) concerning Bnei Yisroel, in order that the people not go astray after idols. How are the appointment of Yehoshua and the institution of the Korban Tamid in any way related?
The Gemara (Sanhedrin 36a) notes that the Korban Tamid is defined as "the korban which is exclusive to Me (Hashem)". This means that, unlike most other sacrifices (which are private), the Tamid is not identified with any one person or limited group. It is anonymous; the only being with whom it is identified is God Himself. Thus, the Tamid, which serves as a regularly-scheduled service of which Hashem is the sole focus, is understandably correlated by the Sifri to the departure of Moshe Rabbeinu and the appointment of Yehoshua. Moshe connected with God through an "apsaklaria ha-meirah" - a "clear lens". His prophecy was not one of images or hints; rather, Moshe's prophecy consisted of the very words of Hashem, and he could enter into a prophetic connection at any time. [Bamidbar 12:8 with Ramchal in Derech Hashem on "Nevuah"] Once this direct, constant and clear connection was to be lost with the demise of Moshe, the Jews would no longer have an intense, focused contact with Hashem; this, in turn, could lead to estrangement and the pursuit of other dieties. Thus, the Korban Tamid was instituted to restore and maintain a regular connection with God. This is what the Sifri means. (The Mussaf offerings, which are commanded immediately after the Tamid, are an extension or addendum ["Mussaf"] to the idea of the Tamid.)
Let's continue with the the theme of connecting to Hashem.
The story of the daughters of Tzelofchod is presented in the parshah, precipitated by the command of tribal inheritance of Eretz Yisroel. Bnos Tzelofchod were noted by Chazal as having been very righteous and as possessive of a deep love for the Land of Israel (Rashi - 27:1), and for this reason did they seek to retain their family's shares in it. These women conveyed a great message, for they demonstrated how that which is normally associated with materialism and focus on self can and should be utilized for connection to God. Bnos Tzelofchod loved the land for its holiness. Rather than viewing it as real estate or in other material terms, they addressed and yearned for its spirituality. Their message is at the core of the entire parshah, for the very theme of Parshas Pinchas is connection to God. Bnos Tzelofchod teach us that we must seek to connect to Him in all ways, and that we are mandated to use the physical to relate to God.
The theme of connecting to Hashem when one is not in a capsule of pure spirituality is thus the theme of Parshas Pinchas. The ability and need to connect to God in a setting of military conquest, without the prophecy of Moshe, as well as in any context which seems to abound in material and/or lack in the pristine spiritual, is the parshah's message.
It is thus understood why the sholom granted to Pinchas for his act serves as the introduction to the parshah, for Pinchas' action and eternal persona represent the ultimate restoration of our connection to Hashem. Under the most dire circumstances, Pinchas performed heroically and with kin'ah for God's Name, reconnecting His people to Him; Eliyahu shall do the same in the time to come. This is why the narrative of Pinchas' reward is severed from the end of Balak and commences this week's parshah.