The 22-year-old di Maria, a 25-million-euro summer signing from Benfica, squeezed a shot past Andres Palop at the near post to maintain Real's 100 percent home record and ensure Jose Mourinho's side begin 2011 within touching distance of Barcelona.
Real had been reduced to ten men on 63 minutes with the sending-off of Portuguese centre-back Ricardo Carvalho, but the hosts overcame their numerical disadvantage to triumph through di Maria's goal.
Sevilla had sensed victory after the dismissal but fell to their fifth successive league defeat and lie down in 11th place eight points off the top four.
Barcelona were much more comfortable crushing Espanyol 5-1 in the Catalan derby at the Cornella-El Prat stadium on Saturday for a tenth successive league win and the double champions top the table at Christmas.
Real were without suspended duo Marcelo and Xabi Alonso but were boosted by the return of Sergio Ramos against the team that launched his career.
In the absence of the injured Gonzalo Higuain, French forward Karim Benzema was given a chance to make an impact on the day of his 23rd birthday, while Sevilla striker Alvaro Negredo had a point to prove against old club Real.
Madrid began with a string of corners but Sevilla had the first real opening with defender Julien Escude heading over from close range on 25 minutes.
Three minutes later di Maria had a swerving shot punched away by Palop in Real's only notable effort on goal in a flat first half.
The Bernabeu were not impressed as Sevilla looked more dangerous with Real goalkeeper Iker Casillas fumbling a free-kick but centre-half Pepe saved the day with a last ditch challenge.
A half-time bust-up between the two dug-outs provided off-the-field spice that was sorely missing on it.
The hosts failed to improve after the break and Negredo should have scored on 57 minutes after latching on to a Luis Fabiano pass but blazed over the crossbar to the relief of the home crowd.
Real were then reduced to ten men just after the hour mark when Carvalho collected a second yellow card for an unnecessary aerial challenge on Negredo.
The dismissal seemed to spur Madrid on and a mistake from goalkeeper Palop, who failed to defend his near post, allowed di Maria to fire home from an acute angle on 77 minutes.
Defender Mouhamadou Dabo was sent off for a reckless challenge on di Maria late on as Sevilla lost their cool and the match.
Elsewhere Atletico Madrid got over their disappointing Europa League exit with a comfortable 3-0 win at lowly Malaga on Sunday to move sixth in the Spanish first division.
Holders Atletico crashed out of the Europa League group stage on Thursday but put that behind them with Portuguese midfielder Tiago scoring a brace to move Atletico two points off the top four.
Tiago, on loan from Juventus, opened the scoring on 22 minutes and grabbed the final goal of the game on 69 minutes as Atletico moved above Getafe on goal difference into sixth and stay in contention for a Champions League place.
It was an 11th defeat of the season for Malaga who stay third from bottom of the standings.
In other matches, in-form Getafe recorded a fourth consecutive league win to go seventh in the Spanish first division following a sensational 3-2 comeback victory over Almeria on Sunday.
Almeria had gone two goals up inside 24 minutes, but Getafe, unbeaten since mid-November in all competitions, stormed back and Ghana international midfielder Derek Boateng scored a 70th-minute winner to lift the club level on points with Atletico.