Luis Suarez and Philippe Coutinho sent Barcelona two goals ahead inside 28 minutes, and it got worse for Malaga - who remain rock bottom of the table on 13 points - in the 30th minute when Samuel Garcia picked up a straight red card.
Ernesto Valverde's side had opportunities to add to the scoring throughout the remainder of the match, but it finished 2-0 following an extremely comfortable night for the visitors.
Barcelona were without the services of Lionel Messi, who withdrew from the squad on Saturday afternoon following the arrival of his third child. Andres Iniesta missed out through injury, meanwhile, meaning that there were starts for Paulinho, Coutinho and Ousmane Dembele.
Barcelona had the first opportunity of the match in the 13th minute, but Luis Suarez, having worked space in a dangerous position, was kept out by a smart save from Malaga goalkeeper Roberto Jimenez.
Luis Suarez was not to be denied less than two minutes later, however, with the Uruguay international heading an excellent Jordi Alba cross into the back of the net to send the league leaders ahead.
Paulinho hit the side-netting after smart work from Luis Suarez in the 21st minute, but it was Coutinho that made it 2-0 in the 28th minute when the Brazilian produced a wonderful flick from a Dembele cross.
It then went from bad to worse for Malaga in the 30th minute when Samuel was handed a straight red card for a terrible challenge on Alba.
The home side had a golden chance to halve the deficit in the 36th minute when Manuel Iturra picked out the head of En Nesiry with a brilliant cross, but the Moroccan somehow headed wide of the post.
Mehdi Lacen then struck over the Barcelona crossbar three minutes later, before Roberto had to stretch his body to keep out a curling Coutinho effort down the other end of the field.
Dembele struck just wide of the Malaga post in the early stages of the second period as Barcelona looked for more goals, before Coutinho had one deflected past Roberto's goal just before the hour mark.
Dembele then tested the handling of the Malaga goalkeeper with a powerful strike in the 66th minute during a period where the home side were struggling to stem the flow of traffic.
Maxime Lestienne passed up a half-chance for Malaga 15 minutes from time when his effort was deflected away, and that was just about the final opportunity of the night as Barcelona's two first-half goals proved key at La Rosaleda.
MALAGA (4-4-2): Roberto; Rosales, Hernandez, Miquel, Ricca; Samuel, Lacen, Iturra, Chory (Lestienne 61'); Rolan (Success 78'), En-Nesyri (Ideye 78')
BARCELONA (4-3-3): Ter Stegen; Roberto (Gomes 74'), Umtiti, Pique, Alba (Digne 77'); Busquets, Rakitic, Paulinho; Coutinho, Suarez, Dembele (Vidal 85')