Jose Mourinho's side, who won 4-3 against Siena last weekend having looked beaten, went behind to two Paulo Barreto penalties in the second half but stormed back despite missing several injured first team players.
Former Lazio striker Pandev kept his cool to net his first Inter goal and then won a spot kick which Diego Milito converted to increase their lead over next weekend's opponents AC Milan to nine points.
"We all knew this was a difficult game. We gave everything to recover. We could even have won but a draw's OK," Macedonia's Pandev, who signed earlier this month, told Sky television.
Bari, ninth in the table, have looked far from overawed in their return to the top flight this season and quickly took the game to the champions.
Their attractive approach was rewarded on the hour when Inter defender Walter Samuel handled the ball when sliding in to stop Riccardo Meggiorini's cross, allowing Brazilian Barreto to slam in the spot-kick.
COMFORTABLE WIN
Barreto celebrated by holding up the shirt of team mate Andrea Ranocchia, whose season has been ruined by injury just when he was threatening a late bid for Italy's World Cup squad.
He was back on the scoresheet just three minutes later, this time slotting the ball into the other corner after Lucio had recklessly brought down Alessandro Parisi.
Inter had only created a few half chances but quickly woke up from their slumber when Pandev latched on to Mario Balotelli's deflected shot to score after 68 minutes.
He was then hauled down in the 74th by Leonardo Bonucci, who was lucky to avoid a red card, and Milito did the rest.
Cagliari earlier moved up to sixth with a comfortable 3-0 win over Livorno in Sardinia.
Joaquin Larrivey headed in a free kick after three minutes and then netted a superb chip from outside the area at the start of the second half before Jeda's header wrapped up the win.
Cagliari, whose president Massimo Cellino has been linked in the media with a bid for West Ham United, are unbeaten in four league games.
