Barca are 14 points clear at the top of the standings with four fixtures left, while Real Madrid have a game in hand and 15 points available to them for the rest of the campaign.
This means that even if Los Blancos do beat Espanyol, Barcelona need just one win from their final four fixtures to wrap up the title, while Real Madrid need a perfect five wins from five games to stand any chance.
In fact, with the two sides playing each other in El Clasico next week, the Catalans will win the title by simply avoiding defeat and denying three points to Real Madrid.
Despite the title potentially being on the line, Barca were not at their best against Osasuna and struggled to create meaningful chances against a solid defensive setup.
They dominated the ball, with 70% of the possession through the game but only managed 13 chances to their hosts' nine, and even created one less clear-cut chance.
The encounter remained locked at 0-0 all the way through to the 81st minute before substitute Marcus Rashford hit a pixel-perfect cross on to the head of star striker Robert Lewandowski, who headed past Sergio Herrera to give Barcelona the lead.
They doubled their advantage five minutes later when Fermin Lopez cut the Osasuna defence with a lovely through ball to Ferran Torres, who slid his finish into the bottom corner.
Osasuna did hit back, though, with Abel Bertones crossing for Raul Garcia to head home in the 88th minute to return a level of respectability to the scoreline.
Elsewhere in LaLiga, Athletic Club prevailed 4-2 over Alaves in a back-and-forth encounter at Estadio Mendizorroza.
The home side started strong with Antonio Blanco putting them ahead in the eighth minute, which they held for the remainder of the first half.
Robert Navarro got Athletic back on level terms instantly after the break, before Nahuel Tenaglia restored Alaves' advantage in the 68th minute.
It was all the visitors from their though, with Oihan Sancet making it 2-2 with his 74th-minute strike before Nico Williams bagged a brace of goals in the 83rd and 87th minutes to secure the come-from-behind win.
Villarreal thumped Levante 5-1 at Estadio de la Ceramica with a devastating second-half blitz.
Georges Mikautadze scored in the 38th minute to ensure the hosts would go into halftime with a 1-0 lead.
Carlos Espi restored parity for Levante in the 51st minute but Villarreal ran away with the game after that.
Alberto Moleiro put them 2-1 up in the 62nd minute before Mikautadze grabbed his second goal of the game six minutes later.
Tajon Buchanan (87') and Nicolas Pepe (90') put the cherry on the cake of a stunning second-half display.
Atletico Madrid beat Valencia 2-0 at Mestalla thanks to goals from Iker Luque (74') and Miguel Cubo (82'), while Samu Costa's 43rd-minute strike was enough to hand Mallorca a 1-0 win over Girona at Estadi Montlivi.