Premier League: Sunderland 1 Everton 1
Dead-ball specialist Sebastian Larsson brought the Stadium of Light to its feet with a fine 67th-minute free-kick but England full-back Baines made no mistake from 12 yards nine minutes later after Connor Wickham had brought down Seamus Coleman.
There was an end-to-end feel for most of the match, but a lack of quality in the final third hindered both teams - a particularly disappointing state of affairs for Samuel Eto'o, who buzzed inventively throughout for Everton in a deep-lying forward position.
The former Barcelona man passed up an early opening himself, while Sunderland's Jordi Gomez and Everton's Romelu Lukaku came closest to breaking the deadlock before Larsson struck.
Baines missed a penalty in last month's 2-1 defeat at Manchester United but Roberto Martinez's team are now unbeaten over six games in all competitions since that reverse.
However, Everton were grateful for the efforts of James McCarthy, who cleared a goalbound header from Wes Brown off the line in stoppage time.
Liam Bridcutt came in for suspended midfielder Lee Cattermole as Sunderland made four changes to the team that won 3-1 at Crystal Palace on Monday night.
An Everton side fresh from a 3-0 UEFA Europa League win over Lille was bolstered by Coleman, Eto'o and Ross Barkley.
The visitors quickly settled into a pleasing passing rhythm and Eto'o linked smoothly with fellow forward Lukaku to blast wide.
Wickham won a fifth-minute corner and the Sunderland forward's header from Larsson's resulting delivery brushed the roof of the net.
Everton midfielder Gareth Barry suffered an early end to his afternoon on a stretcher when Gomez caught his right ankle with a late tackle, aggravating a complaint the former England player carried into the match.
Sunderland were growing in confidence by the time Sylvain Distin hacked a Gomez cross out of the goalmouth, while Aiden McGeady offered Everton's response by sending a rasping drive narrowly over the top corner.
Barkley and McGeady exchanged passes to force a fine block from Bridcutt in the 35th minute before an error from Barry's replacement Darron Gibson saw Gomez force a fine save from Tim Howard.
Bridcutt largely impressed during the opening exchanges of the second half but the former Brighton player under hit an ill-advised backpass, his blushes spared as Costel Pantilimon rushed from his goal to deny Lukaku.
Referee Lee Mason entertained the Stadium of Light masses when he fell over due to a collision with McCarthy, shortly before Baines forced a far more significant tumble from Sunderland substitute Will Buckley - on for the ineffective Adam Johnson.
Larsson stepped up to curl a trademark effort beyond Howard, aided by a disorganised Everton wall, but Sunderland's lead proved short-lived.
Wickham lunged in to bring down Coleman, who dashed into the area on the end of a wonderful Eto'o pass, and Baines crashed home from the spot following prolonged complaints from the Sunderland players.
Sunderland edge three points clear of the relegation zone, although they might have been better off as Brown saw an injury-time header cleared off the line by McCarthy.