Xavi Hernandez's Barcelona side climbed 14 points clear of second place Real Madrid with a narrow 1-0 win over Osasuna.
The visitors had debutant Jorge Herrando sent off in the first half for a professional foul on Pedri, as they sat deep and tried to frustrate hosts Barcelona.
Visiting goalkeeper Aitor Fernandez kept the leaders at bay in the second half but eventually substitute Alba, who has had reduced minutes this season, sliced home a volley to snatch a late victory.
"For a full-back I've had the luck of scoring many goals," Alba told DAZN.
"It was important to win, it was a hard game against a side having a good season.
"We haven't won La Liga for a while and for someone from here, it feels very good."
Osasuna coach Jagoba Arrasate rotated heavily to rest players ahead of the Copa del Rey final against Madrid on Saturday, while Barca started with the same side which crushed Real Betis at the weekend.
The Catalans failed to carve out many clear opportunities in the first half against their defensive opponents.
The best chance fell to Pedri after left-back Alejandro Balde found him a few yards out from goal but he did not connect with the ball well, scuffing a shot wide.
Osasuna were reduced to 10 men before the half hour mark when Herrando pulled down Pedri as he ran in on goal.
The visitors might have been reduced to nine men as goalkeeper Aitor Fernandez collided with Raphinha outside the area as the Brazilian burst through, but the referee decided both players were to blame.
Ronald Araujo powered a header narrowly over the bar from Raphinha's corner, while the Brazilian whipped a free-kick onto the roof of the net.
Xavi brought on Ansu Fati after 35 minutes for Gavi, who appeared to take a knock, and the forward came close at the start of the second half but Fernandez denied him.
- String of saves -
Frenkie de Jong should have sent Barcelona ahead but fired straight at the goalkeeper from six yards out when Pedri found him.
Barcelona's frustration grew when Fernandez saved from Fati again and substitute Ousmane Dembele sent a shot wide from close range.
La Liga's top scorer Robert Lewandowski had another quiet night at the office and when he did get a chance, Fernandez foiled him too.
Ferran Torres almost scored when he deflected a clearance narrowly wide of the far post, with Osasuna clinging on by their fingertips.
When Lewandowski found the net with 10 minutes remaining it was ruled out for offside.
Eventually the breakthrough came with five minutes to go, with substitute Alba volleying home his second goal of the season after De Jong headed the ball into his path, sparking vigorous celebrations.
"It was already a tricky game and with a man less, much more so," said Arrasate.
"Osasuna gave a lesson on what it means for us to compete."
اخلاء مسئولية! : هذا المحتوى لم يتم انشائة او استضافته بواسطة موقع اخبار الكورة و اي مسؤلية قانونية تقع على عاتق الموقع مصدر الخبر : بي ان الرياضية  , يتم جمع الاخبار عن طريق خدمة ال RSS المتاحة مجانا للجمهور من المصدر : بي ان الرياضية  مع الحفظ على حقوق الملكية الخاصة بمصدر الخبر.