Fearnley ranked in the top 600 in early 2024, but won four ATP Challenger titles in September, making it to the top 100.
He has won five wins in eight games in Clay since last month's first game.
Fearnley swapped games with top 25 player Lajovic in each of the opening four games.
But he broke the game by taking a 5-4 lead and took the game in Game 2.
After Lajovic initially mastered the victory in 72 minutes, Fearnley won six straight games.
Cameron Norrie faced Swiss player Dominic Stricker after former UK No. 1 passed the qualifying match late Monday.
