Borini, who was once on the books at Stamford Bridge, converted an 82nd-minute penalty after Cesar Azpilicueta had fouled substitute Jozy Altidore to end Jose Mourinho's 77-match unbeaten run in home league encounters as Chelsea boss.
It is the second time this week that Sunderland have bolstered Liverpool's cause following the 2-2 midweek draw with third-placed Manchester City.
And the result simultaneously provided a huge lift to the survival chances of Gus Poyet's side, who are now only three points from safety.
Having scored a brace in Wednesday's encounter at the Etihad Stadium, Connor Wickham struck in the 18th minute to cancel out a Samuel Eto'o opener for Chelsea.
An error from Vito Mannone had handed City a point but Chelsea found Sunderland's goalkeeper in superb form as he produced an inspired string of saves before half-time.
Eto'o and substitute Demba Ba spurned chances in the second period before Borini struck - meaning that Liverpool can now open up a five-point cushion ahead of the top two's crunch meeting at Anfield next week if they beat Norwich City in Sunday's early kick-off.
Chelsea went into the match boasting nine consecutive home clean sheets - a record that 41-year-old goalkeeper Mark Schwarzer had to protect on his Premier League debut, with Petr Cech laid low by a virus.
The veteran Australian watched Borini fire a seventh-minute drive wide following some impressive hold-up play from Wickham.
Eto'o was then denied by a perfectly timed sliding tackle from Santiago Vergini but responded to volley home the resulting 12th-minute corner.
The lead was soon wiped out, though, when Schwarzer spilled Marcos Alonso's dipping drive and Wickham reacted quicker than John Terry to convert the rebound.
Slack set-piece marking almost undermined Sunderland again in the 37th minute but Mannone grasped Branislav Ivanovic's header at the second attempt via the crossbar.
There was little let up for the Italian goalkeeper as half-time approached and he produced impressive saves to thwart Willian and Nemanja Matic from close quarters.
In the 44th minute, after Mannone had parried from Willian, Sebastian Larsson out-muscled Ramires as the Brazilian looked to convert into an empty net.
Perhaps still suffering the frustration of that incident, Ramires was then fortunate to escape punishment when he struck Larsson with his elbow.
A breathless opening period concluded when Chelsea defender Azpilicueta made a last-ditch challenge to deny Adam Johnson having conceded possession to the Sunderland winger.
Chances continued to flow for Chelsea and Eto'o guided the ball wide after Willian had driven forward on the counter-attack in the 48th minute.
Mourinho sent on Ba in place of the ineffective Oscar but the player who netted vital goals in the recent triumphs over Paris St Germain and Swansea City found the Midas touch had deserted him, losing his footing when trying to get on the end of Willian's 66th-minute cutback with the goal gaping.
Sunderland weathered further pressure before Azpilicueta clumsily bundled Altidore to the floor and Borini stole the points from the spot with eight minutes left.
Poyet's team remain bottom of the table but three of their four remaining games are at home against fellow strugglers Cardiff City, West Brom, Swansea City.
