The Toffees' seventh win in a row moves them up to fourth in the table, two points above Arsenal with five games to go in the race for a Champions League qualifying berth. They have now amassed their highest points tally - 66 to date - in a single Premier League campaign, surpassing the 65-mark they reached in 2007-08.
In contrast, the Black Cats remain bottom with no wins in eight games. They are now seven points from safety, although they do have two games in hand on the three clubs immediately above them.
In truth, defeat was somewhat harsh on the hosts, although Everton may feel they deserved a break against Gus Poyet's men after losing 1-0 in the Boxing Day meeting at Goodison Park after an inspired display by Vito Mannone.
The Sunderland goalkeeper had his moments in this game too, but could not keep the ball out after it deflected off Brown when Gerard Deulofeu played it across from a tight angle with a quarter of an hour remaining.
Roberto Martinez made just one change to his starting line-up. Deulofeu replaced Kevin Mirallas as the Everton manager otherwise kept faith with the men who started last Sunday's 3-0 win over Arsenal.
Poyet left out Carlos Cuellar and Santiago Vergini, while Liam Bridcutt was absent after his partner went into labour. Skipper John O'Shea, Jack Colback and Connor Wickham all came in, with Colback and full-back Phil Bardsley included despite the manager's admission that they look likely to leave the club at the end of the season.
The Stadium of Light was far from full but the 38,445 fans in attendance did see their team make a decent enough start, with Ki winning a free-kick via a James McCarthy foul. Fabio Borini blasted the set-piece over the bar.
After Deulofeu had dallied when played through on goal, Steven Naismith cleverly turned Brown in the box to set himself up for a great chance - but the in-form Scotland striker lashed his shot too high.
Adam Johnson was then booked on 18 minutes for a pull on Leighton Baines.
John Stones kept the scoreline blank with a timely intervention just after the half-hour mark, the young defender getting between the goalline and Borini's shot on a tight angle after the Italian had taken the ball around Tim Howard following Baines' short backpass.
Having stolen a yard on Brown, Romelu Lukaku snatched a shot across goal and wide of the far post three minutes later after being set up by Baines, as Everton looked to finish the first half strongly.
Poyet was left fuming just before the interval, however, when referee Lee Probert missed what looked to be a blatant bodycheck on Johnson by Baines.
Seamus Coleman and Bardsley were both booked early on in the second period, for fouls on Borini and Naismith respectively.
Bardsley's header from a corner had to be cleared by Everton, before Ross Barkley came on to replace Leon Osman in the 58th minute.
In the 62nd minute, Mannone attempted to head clear a long kick by his opposite number Howard but only succeeded in finding Naismith. However, the Scot volleyed wide with an open goal beckoning.
After Johnson fired wide at the other end, Mannone saved well from Barkley after he stabbed Sylvain Distin's cross towards goal but, after Seb Larsson replaced Colback, disaster struck for Sunderland.
Deulofeu got past Marcos Alonso to the byline on the right and his cross hit Brown before squirming in at the near post. It was the seventh own goal Sunderland have conceded so far this season.
Howard saved from Ki and Borini also went close before the final whistle blew.
Everton have home games against Crystal Palace on Wednesday and Manchester United on Sunday, while Sunderland travel to face Manchester City in midweek before heading to Chelsea on Saturday.