important verse from Srimad bhagvadgita-6

In the beginning of creation, the Lord of all creatures sent forth generations of men and demigods, along with sacrifices , and blessed them by saying, "Be thou happy by this yajna [sacrifice] because its performance will bestow upon you all desirable things."........3:10

sri kesava kasmiri translates the verse very beautifully here:
Here Lord Krishna reveals the words of Prajapati or Brahma the creator of the forms and categories of material beings and the arranger of the material manifestation. Here it states that one desiring liberation from bondage should perform selfless actions with the thought of appeasement and propitiation to the Supreme Lord. Now Lord Krishna is infering that he teaches this knowledge of propitiatiopn to His devotees only. This is because Brahma has given facilty for beings other than the devotees to worship in appeasement lesser gods such as the demi-gods. Thus after Brahma created mankind he instructed to perform selfless actions in the spirit of worship of the Supreme Lord and this will be for you sacrifice. Sacrificing the desires for reward and attachment to the results and in this way mankind will flourish and prosper. The actual understanding is that this spirit of sacrifice perfromed with faith acording to ones status and stage in life will bequeath all auspiciousness in this life and the next life. Such instructions for such wishfulfilling actions and the confusion that might arise to due to them from statements of non- attachment earlier in this chapter in verses four, seven and seventeen as well as refering to delighting in the atma or soul in this chapter in verses three and nineteen is empasising different approaches to the same goal based on qualification so there is no contradiction.
In continuation of this talk lord Krishna says in next verse that The demigods, being pleased by sacrifices, will also please you; thus nourishing one another, there will reign general prosperity for all.


To answer the question how will yagna or worship fulfill one's prayers?
Lord Krishna reponds that the devas or demi-gods nourished by the oblations offered will in turn mutually reciprocate fulfilling all one's prayers with prosperity and abundance. Gratifying each other as such human and deva will all attain the fulfillment of their desires.
So by appeasement of demi -Gods one can have fulfillment of prosperity here prosperity meaning material fulfillment. Hence the bondage is not gone, but can enjoy the fruits of swarga for some days and again the same life . But for temporary relief there is an arrangement of Demi-gods so do selfless yagyam.