The force also destroyed two Pakistani posts in retaliation to the killing of its jawan in unprovoked firing on Wednesday.
IG BSF, Jammu frontier, Ram Awtar told PTI that troops observed movement of two-three persons along the IB near Nikowal Border Out Post in Arnia sector around 0545 hours.
They challenged them and opened fire resulting in the death of one intruder, he said adding, the deceased was in his thirties.
The other intruders managed to escape, he said.
A BSF spokesman said two Pakistani mortar positions were "located, targeted and destroyed by BSF troopers yesterday night only. The coordinated precision fire of BSF troopers silenced Pakistani guns".
On Wednesday, BSF jawan R P Hazra was killed in unprovoked firing by Pakistan, the first this year, in Samba sector of Jammu and the force had since then launched retaliatory fire.
Pakistan troops also violated ceasefire by firing and shelling posts along the LoC in Rajouri district last night and shelling exchanges continued throughout the night along the IB.
"Post death of BSF trooper Head Constable R P Hazra from unprovoked fire by Pak forces on Jammu IB in Samba sector yesterday, the retaliation continued till late night", a BSF officer said.
"The unprovoked fire from Pakistan started first from small arms which later coupled with mortar shelling throughout the night", he said.
BSF troopers consolidated their positions, located and marked Pak firing positions and started precision targeted fire, he said, adding "the coordinated precision fire of BSF troopers silenced Pak guns".
BSF maintains extra vigil on IB to negate intrusion attempts which is aided by forces on the other side of the IB, he said, adding that firing across the IB is most of the time a diversionary tactic for facilitating intrusion.