Barca has not lost since a 2-1 defeat to Sevilla on October 23, its run comprising of 23 wins and five draws, claiming the Club World Cup, reaching the last 16 of its defense of the Champions League and a commanding position in the league, with a game in hand over second-placed Atletico Madrid.
Arch-rival Real Madrid later cut its deficit in third to four points with a 2-1 win at Granada, but its 4-0 defeat in El Clasico was another highlight of Barcelona's relentless run.
The Catalan giant can set a new record by avoiding defeat in the Mestalla to Valencia in the second leg of their Copa del Rey semifinal on Wednesday.
Given Valencia's dismal form under new coach Gary Neville, with Sunday seeing a 1-0 defeat at Real Betis, coming hard on the heels of the 7-0 first leg thrashing by Barcelona, a new best looks firmly on the cards.
Neville, winless in La Liga in nine games, leaving aside his side's humiliation in the Nou Camp last week, is under severe pressure with his side slipping into the relegation zone.
"It's just not going for us at the moment. That was a pretty solid away performance. I continue to work, I continue to have belief and any conversations with the owners are between me and the owners," former England international Neville told reporters after another defeat.
Barcelona's win at bottom club Levante was far short of its best performance of the season, with a David Navarro first half own goal from a Jordi Alba cross all it had to show from the game until Luis Suarez made the three points safe in stoppage time for a 10th straight win in all competitions.
"We're getting things right. It's quite some achievement to go 28 games without losing. We have to stay top," Alba told the official Barcelona website.
Coach Luis Enrique, taking charge for the 100th time, cautioned against carried away by records at a crucial stage of the season.
"I am interested in collective goals that we have as a team. Statistics are good but there is a long way to go," he said after his team matched the record set by his predecessor Pep Guardiola's team in the 2010/11 season.
Real, missing the still sidelined Gareth Bale, was later given a real fright by Granada, despite taking the lead through a 30th minute goal from the prolific Karim Benzema, who has now scored eight goals in his last six games.
The home side kept pressing for an equalizer and was rewarded on the hour mark when Youssef El-Arabi scored with a low right-footed shot.
With Cristiano Ronaldo largely kept quiet, Los Blancos had to rely on Croatian midfielder Luka Modric to cap a fine personal performance with a superbly struck winner in the 85th minute.
It was his first La Liga goal since September 2014 and provided Zinedine Zidane's team with an absolutely precious three points in the three-way Spanish title race.
Costa denies Man Utd
Sunday's action in the English Premier League saw a 1-1 draw between Chelsea and Manchester United at Stamford Bridge with Diego Costa equalizing in injury time for the defending champion.
United, improving recently under Louis van Gaal, produced one of its best performances of the season against a fierce rival and took a deserved lead when youngster Jesse Lingard scored with a strike on the turn in the 61st minute.
Three points would have taken United to within four points of fourth place, but Cesc Fabregas found Costa, who rounded David de Gea for his seventh goal in eight games.
Chelsea stayed in 13th, no less than 23 points adrift of surprise leader Leicester and 17 points outside of the final Champions League spot held by Manchester City. The Blues also lost defender Kurt Zouma to a serious knee injury in the second half.
In the early kick off, Arsenal hauled itself back into the title race with a 2-0 win at Bournemouth, with two goals in quick succession in the first half from Mesut Ozil and Alex Oxlade-Chamberlain.
The home side forced a fine save from Petr Cech in the second half, but the Gunners were largely untroubled in claiming a vital victory, drawing level on points with second-placed Tottenham Hotspur, but five points behind Leicester.
The top four meet in clashes next weekend, with Leicester at Arsenal and Manchester City hosting Tottenham.