Pique was sent off in the 25th minute for a wild challenge on Rafa Lopez.
Marquez walked at the end after bundling over Kepa for a last-minute penalty scored by Roberto Soldado but the game was effectively over by then.
Lionel Messi opened the scoring in the seventh minute and Xavi netted in the 67th as Barca continued to create the clearer chances despite their numerical disadvantage.
"You only manage this with commitment, a great deal of belief and by running a lot. The players have been marvellous," Barca coach Pep Guardiola told reporters.
"We played a very good game and it was one of the best performances we've put in."
The unbeaten champions moved on to 55 points from 21 games, and remained five ahead of second-placed Real, who comfortably swept aside Espanyol.
Sergio Ramos headed in from a freekick early on and Kaka doubled the lead after Carlos Kameni could only parry a Raul header in the 30th minute. Gonzalo Higuain returned from injury to grab a third at the end.
MESSI CURLER
Getafe attempted to take the game to Barca by starting with two strikers but it was the home side who struck first when Messi curled in a shot from the edge of the area for his 16th goal of the campaign.
Barca were just starting to take control when Pique was dismissed, and Guardiola held off from making a defensive substitution until early in the second half.
Messi, Zlatan Ibrahimovic and Seydou Keita all went close before the Argentine World Player of the Year broke away on a counter-attack and squared for Xavi to give them a two-goal cushion.
Getafe, who have a King's Cup semi-final second leg against Sevilla next week, had plenty of possession but created little until they were gifted a penalty in added time.
Earlier, Valencia spoiled Onesimo Sanchez's debut as Real Valladolid coach, winning 2-0 to stay third with 42 points.
Struggling Valladolid, who are 17th, sacked Jose Luis Mendilibar on Monday but the change failed to spark an immediate revival in their fortunes at the Mestalla.
Ever Banega was at the centre of most of Valencia's best moves and cracked in a fierce drive for the opener after eight minutes.
The Argentine midfielder then crossed for David Villa to head his 15th league goal of the campaign in the 29th. The hosts squandered several more chances after the break.
