Jose Arnaiz opened the scoring for Osasuna, before Lionel Messi's long-range strike and his 23rd La Liga goal put him ahead.
Real Madrid have won La Liga this season for the 34th time.
'Hardly spectators will continue to visit stadiums in Spain'
Osasuna ended the match with 10 men on the pitch, after Enric Gallego was sent off.
Roberto Torres scored Osasuna's second in stoppage time after Kike Barja's cross found the back of the net.
Barca have not lost at home since November 2018, after beating Real Betis 4-3.
Results of Week 37 of La Liga on Thursday.
1:Eibar 3-1 Real Valladolid
2:Athletic Bilbao 0-2 Leganes
3:Barcelona 1-2 Osasuna
4:Real Betis 1-2 Deportivo Alaves
5:Celta Vigo 2-3 Levante
6:Real Mallorca 1-2 Granada
7:Real Madrid and Villarreal C
8:Real Sociedad 0-0 Sevilla
9:Valencia 1-0 Espanyol
10:Getafe 0-2 Atletico Madrid
Top scorers in this year's competition:
1:Lionel Messi Barcelona 23
2:Karim Benzema Real Madrid 21
3:Gerard Moreno Villarreal 16
4:Raul Garcia Athletic Bilbao 16
5:Luis Suarez Barcelona 15
6:Lucas Ocampos Sevilla 14
7:Iago Aspas Celta de Vigo 14
8:Alvaro Morata Atletico de Madrid 12
9:Ante Budimir Real Mallorca 12
10:Roger Marti Levante 11
11:Willian Jose Real Sociedad 11
12:Santi Cazorla Villarreal 11
13:Lucas Perez Deportivo Alaves 11
14:Jaime Mata Getafe 11
Week 38 games to be played on July 19:
1:Deportivo Alaves and Barcelona
2:Atletico Madrid and Real Sociedad
3:Espanyolda Celta Vigo
4:Osasunada Real Mallorca
5:Sevilla and Valencia C.F.
6:Real Valladolid and Real Betis
7:Villarreal and Eibar
8:Leganesda Real Madrid CF
9:Levante da Getafe CF
10:Granada and Athletic Bilbao
List of La Liga winners:
1:Real Madrid 34
3:Atletico Madrid 10
4:Athletic Bilbao 8
6:Real Sociedad 2
7:Deportivo La Coruna 1
8:Sevilla FC 1
9:Real Betis 1
The trophy Barca hope to win this year is the Champions League.
Barca will host Napoli in the last 16 of the competition on August 8.
In the first match they went to a 1-1 draw in Italy.
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