Charlton's precious victory was preserved in the last minute of normal time by a stunning save from Scott Carson, who dived to his left to push away a goalbound effort from Andy Cole.
The Addicks had previously gained only a single point all season away from home but there was no denying that, on the day, they were the better team in a match of disappointing quality which only sprung to life in the last 20 minutes.
Portsmouth badly missed the guile and tenacity of suspended midfielder Gary O'Neil, while Charlton manager Alan Pardew found that his tactics based on a 4-5-1 system paid off handsomely.
Charlton overcame a nervous start to have the better of the first half and, although Portsmouth increased the pressure after the break, Pardew's men always looked dangerous on the break.
Charlton's new left-back Ben Thatcher was booed from the first minute by Portsmouth supporters in retribution for his fearsome challenge on Pedro Mendes, which earned him an eight-match ban and left Mendes unconscious in hospital earlier this season.
Thatcher showed no signs of nerves or being intimidated and played a full part in a solid defensive performance, alongside the impressive Talal El Karkouri and Hermann Hreidarsson.
Pompey goalkeeper David James made an outstanding first-half save to keep out a header from Bryan Hughes as Portsmouth struggled to find any kind of rhythm.
Apart from a shot on the turn by Cole, the home side had little to show for their efforts and it was no surprise when, after 54 minutes, Pompey manager, Harry Redknapp, took off the struggling Sean Davis and replaced him with Rudolphe Douala, although it made little difference to the outcome.
Nwankwo Kanu went close with a couple of second-half chances for Portsmouth but it needed a spectacular tackle from Sole Campbell to deny Dennis Rommedahl when the Danish winger raced clear in the 73rd minute.
But Charlton were not to be denied and, in the 78th minute, Faye took a return pass from Hughes and his shot looped beyond the reach of goalkeeper James.
As Portsmouth's desperate search for an equaliser grew in intensity, Charlton had three players booked, Osei Sankofa and Faye for fouls and Carson for timewasting soon after his great save.
Cole should have done better soon after Carson had denied him but with a free header from a centre by Matt Taylor, his effort flew harmlessly over the bar.
Charlton manager Pardew was acutely aware that his side had picked up only one point from their trips away this season, at Newcastle, but the vital away win will lift spirits.
Pompey boss Redknapp also replaced Kanu, who had made little impression, with the extra pace of Benjani Mwaruwari, but the Charlton defence was in no mood for surrender.
Outstanding for Charlton was hard-working midfielder and captain, Matt Holland, who got through a prodigious amount of effort.
At the back, Hreidarsson and El Karkouri gave Kanu and Cole few openings.
Redknapp gave a debut on the right side of midfield to new signing Lauren from Arsenal, making his first Premiership appearance for almost exactly a year.
He was not seen at his best in midfield, while Djimi Traore was caught out of position at left-back on several occasions as Charlton grafted to success.