He stabbed one of the boys. The other, believed to be of a similar age, was uninjured. The injured boy was pronounced dead soon after arrival at Whiston Hospital.
Police said the boy was playing with two friends from the Huyton area when they were chased by a man after they taunted him. They raced over a school field and ended up in St Agnes Road, where they thought they had escaped.
But the boys later told police the man caught up with them and seemed to punch the 14-year-old.
A police spokeswoman said: "They thought he'd been punched because he went flying over a wall but then they realised he'd been stabbed because there was blood on his clothing." The two boys knocked on a window for help as the boy staggered on to the street and collapsed.
Residents rang an ambulance and gave him first aid but he died soon after arriving at hospital.
The boys gave a description of the knifeman to police.
A 36-year-old man is being questioned.