The three-times World Player of the Year took his tally in his last six matches - five for Barca and one for Argentina - to 16, including a record five-goal haul in Wednesday's 7-1 Champions League victory against Bayer Leverkusen.
Real had to come from a goal down to beat Real Betis 3-2 in Seville on Saturday, when Cristiano Ronaldo scored twice and they set a club record of 10 successive wins on the road in coach Jose Mourinho's 100th game in charge.
With 12 matches left, Real have 70 points, with Spanish, European and world champions Barca on 60. Third-placed Valencia dropped further behind on 44 after letting slip a two-goal lead to draw 2-2 at home to Real Mallorca earlier on Sunday.
"We had to put in a lot of effort," Barca coach Pep Guardiola told a news conference.
"We did things well on a pitch that did not help the circulation of the ball," he added, in a reference to the poor state of the playing surface. "They put nine men behind the ball and that is never easy."
BAPTISM OF FIRE
Messi fired Barca ahead in the 29th minute at the Sardinero when he slid in to turn a Cesc Fabregas centre into the net from close range.
He doubled the lead with a 56th-minute penalty following a foul on Fabregas, his 30th league goal of the campaign, leaving him two behind top scorer Ronaldo, and his 50th in all competitions this season.
He is only three short of his best haul for a season of 53, achieved last term, and needs five more to equal Cesar Rodriguez's club record of 235 goals at the age of only 24.
Winger Isaac Cuenca went close to a third for Barca shortly after Messi's second, striking a powerful shot that cannoned back off a post, before Santander goalkeeper Mario Fernandez denied Messi a hat-trick with a fine save from the Argentine's rasping left-foot drive.
"He is a different player to the rest of the world," Fabregas, who played in Barca's youth ranks with Messi, told reporters.
"It's a pleasure to play with him because it gives you that extra confidence that all champion teams need," the former Arsenal captain added.
"He is a very humble and hard-working player who simply loves playing football."
The match was a baptism of fire for Alvaro Cervera, who was appointed as Santander's third coach this season on Friday, and the defeat left the club in 18th place on 24 points, three behind Villarreal, who host Getafe on Monday.
Osasuna leap-frogged Athletic Bilbao into sixth when they beat the visiting Basques 2-1 in Sunday's late kick-off, while Atletico Madrid and Espanyol climbed to eighth and ninth respectively after home wins against Granada and Rayo Vallecano.
Defender Miranda and striker Radamel Falcao scored in a 2-0 win for Atletico, while Nigerian forward Kalu Uche grabbed a hat-trick in Espanyol's 5-1 drubbing of Rayo.
