Sean Dyche's Clarets began brightly in Saturday's Premier League clash at Turf Moor but Leeds held firm and went 1-0 up through Mateusz Klich's fine finish one minute before the break.
Harrison then doubled the Whites advantage on the hour mark when producing what appeared to be a sublime and instinctive flick to turn a low Gjanni Alioski shot past Burnley 'keeper Bailey Peacock-Farrell.
Harrison then laid on two superb passes for substitute Rodrigo to net a late brace meaning the Whites winger finished the game with two assists and a goal but modest about his achievements.
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"I think my goal was a bit lucky but I think as a team we can be very happy with that performance," said Harrison, speaking to BT Sport.
"I meant to just direct it towards goal but I wasn't sure if I was offside or not and luckily for us I was onside.
"Rodri makes some brilliant runs and you can see the quality that he has to finish it off. Two class finishes from him."
Reflecting on his side's improvement as the game developed, Harrison reasoned: "In the first five minutes of the game they were all over us.
"They kept us in our box and we found it very difficult for us to play out.
"But I think we defended well and just managed to get through that tough period as a team and after that settled down and played our game."
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Thank you Laura Collins