The Poland international registered in the 61st minute of the contest, and his effort proved to be the difference between the two sides, with Hansi Flick's side picking up a vital three points at their temporary home.
Barcelona are now only four points behind leaders Real Madrid in the La Liga table, with the Catalan giants taking full advantage of the capital outfit's shock defeat to Espanyol on Saturday night.
As for Alaves, their 11th league defeat of the campaign has left them down in 18th spot in the division, two points behind 17th-placed Espanyol, with the team firmly involved in a relegation battle this term.
SPORTS MOLE'S VERDICT
This was not vintage Barcelona by any stretch of the imagination, but they simply had to win, with Real Madrid's surprise defeat at Espanyol opening the door for the Catalan team to move to within four points of the summit.
That was the case, with Lewandowski's goal the difference, but it was Lamine Yamal that stole the show with a fine display.
Barcelona have had their issues at their temporary home stadium this season, so it was about getting over the line on Sunday afternoon, and the fact that Alaves failed to register a shot on target was a huge positive.
Flick's team had 11 shots, four of which were on target, while they dominated the possession, so the win was fully deserved, and this could go down as an important weekend in the title race, with three teams firmly in the running for the championship at this stage.
BARCELONA VS. ALAVES HIGHLIGHTS
61st min: Barcelona 1-0 Alaves (Robert Lewandowski)
Barcelona make the breakthrough in the 61st minute of the match, as Lewandowski taps in from close range after Raphinha had an effort deflected towards the far corner - it is a hugely important moment in this contest.
MAN OF THE MATCH - LAMINE YAMAL
Lewandowski scored the only goal of the match, but it was another Barcelona attacker that made the biggest impression, with 17-year-old Yamal once again demonstrating why he is one of the best youngsters in world football.
The Spain international managed an incredible 10 successful dribbles, while he also provided three key passes, with Alaves struggling to deal with the teenager when he had possession of the ball.
BARCELONA VS. ALAVES MATCH STATS
Possession: Barcelona 71%-29% Alaves
Shots: Barcelona 11-3 Alaves
Shots on target: Barcelona 4-0 Alaves
Corners: Barcelona 5-2 Alaves
Fouls: Barcelona 8-20 Alaves
BEST STATS
WHAT NEXT?
Barcelona's attention will now switch to the Copa del Rey, with the Catalan outfit facing Valencia in the quarter-finals of the competition on Thursday night, before returning to La Liga action away to Sevilla next Sunday.
Alaves, meanwhile, will resume their league season at home to Getafe next Sunday, and the Basque outfit can take plenty of positives from what was a solid performance against Flick's team.
Written by
Matt Law