This title “God of the Breakthrough”, which is found in a popular Gospel song, comes from 2 Samuel and 1 Chronicles:
2 Sam 5:20
And David came to Baal-perazim, and David defeated them there. And he said, “The Lord has burst through my enemies before me like a bursting flood.” Therefore the name of that place is called Baal-perazim.
 5:20 Baal-perazim means lord of bursting through
1 Chron. 14:11 And he went up to Baal-perazim, and David struck them down there. And David said, “God has broken through my enemies by my hand, like a bursting flood.” Therefore the name of that place is called Baal-perazim.
Baal-perazim means Lord of breaking through
David is making a word-play. In Hebrew the verb ‘perets‘ (burst through) comes twice in the verse. David says “parats Yhwh” (Yahweh burst through) like “perets mayim” (bursting of waters). Baal is a common word for master, or Master, meaning a god or (to Jews) God.
It is possible that David altered and gave a new meaning to an existing local Canaanite name, but it seems more likely to be an example where the writer uses the name known later at the time of the writer of the book, even though this name had not yet been given to the place when David came there — similar examples are in Gen. 14:14, 1 Sam. 4:1 and 5:1, and Judges 15:9, 14. So the text means “And David came to [what is today called] Baal-perazim…”.
Breakthrough in prayer and life.
The example of David in 2 Sam.5:20 is in fact a good example to be referenced in a Gospel song. This battle with the Philistines comes at a critical point for David and marks the moment which Jerusalem became a royal city. David had started his work of king at the age of 30 (the age when Christ was baptised, and the age of a priest), and had already reigned over Judah seven years and six months from Hebron, and this ‘breakthrough’ marks the beginning of his reign at Jerusalem, where he reigned over all Israel and Judah thirty-three years (2 Sam.5:5). David’s move to Jerusalem brought the Philistines against the city, and it was prayer to God (2 Sam 5:19) which gave David the confidence to fight and win.