As Yaakov was in battle with the angel, the malach said, “Let me go for it's morning" Chazal tell us that he meant that 'it's time for me to sing shira to Hashem'.
The Koshnitzer Maggid asks - If he knew that he has to sing shira at a appointed time why did he pick a fight with Yaakov so close to that time? Wouldn’t it have been smarter for him to fight with Yaakov after he sang shira?
The answer lies in the understanding of who the angel was and what his tachlis- purpose on this world. Chazal teach us that the angel was the 'sar shel Esav' also known as the yetzer horah.
On the last day of creation it says, (bereishes 1;31) "Hashem saw all that he had made, and lo! It was very good." The medrish explains that 'It was good' refers to the yetzer tov, while the 'very good' refers to the yetzer horah. The meforshim explain that life would be nice and calm without an evil inclination, but without any tests we wouldn't be able to grow. Being challenged by the yetzer horah and overcoming it is what makes this world 'very good'. The whole purpose of creation in general and the evil inclination in particular is to help us grow by overcoming the obstacles we are faced with and when we do, the evil inclination has accomplished it's purpose of creation.
Shira is sang to Hakodosh borech hu when a mission has been accomplished. The precise second that the angel saw that he could not win over Yaakov, that in fact Yaakov had overcome his fight with the yetzer horah, his mission was completed successfully and thus was able to sing shira to Hashem.