BARI - Goran Pandev opened his scoring account for Inter and Diego Milito fired in a crucial penalty as the league leaders came from two goals down to hold Bari at the Stadio San Nicola.
José Mourinho's team followed up last weekend's fightback at Siena with another gritty performance, battling from behind after Barreto twice scored from the spot.
The draw leaves Inter nine points clear at the top of the table ahead of Sunday's fixtures.
Inter, playing 4-2-3-1 for the third time in as many matches in 2010, fired an early warning sign to the Galletti when Sneijder narrowly missed with a low deflected shot from Milito's pull-back in the opening seconds.
Backed by a vociferous home crowd, Bari were increasingly efficient on the counter-attack in an end-to-end first half, Julio Cesar saving Alvarez' close-range effort with his legs before getting down to block Parisi's angled effort aimed at his near post.
Inter had the patience to wear down a spirited Bari side and Sneijder forced Gillet into a spectacular save with a magnificent curling free kick from the left channel early in the second half. From the corner Milito saw his shot spin off Bonucci, with Cordoba's follow-up going wide.
Just when it looked like Inter had stepped up a gear, Bari were awarded a penalty after Samuel handled Meggiorini's diagonal shot. Barreto stepped up to the spot and sent Julio Cesar the wrong way to leave the Nerazzurri with an uphill task.
Worse was to follow less than two minutes later when Rosetti pointed to the spot after Parisi went down under a challenge from Lucio. Barreto picked the opposite corner to double his team's lead.
Mourinho made a double change, bringing on Santon and Quaresma for Samuel and Muntari, and the Nerazzurri were soon back in the game when Pandev stabbed home from the edge of the six-yard box for his first goal in black 'n blue and fiftieth in Serie A.
Unfazed, Inter saw their never-say-die attitude rewarded soon after when Milito scored from the spot after Pandev was tripped in the area by Bonucci.
Inter academy product Riccardo Meggiorini came close to a late winner for Bari, his low shot from distance finishing inches wide.
Bari 2-2 Inter (HT: 0-0)
Scorers: Barreto (2 pens), 60, 63, Pandev 69, Milito (pen) 74.
Bari: 1 Gillet; 15 Belmonte, 5 A.Maisello, 19 Bonucci, 21 Parisi; 90 Alvarez (88 Kamata 89), 14 Gazzi, 16 Donati, 11 Koman (7 Rivas 77); 69 Meggiorini, 10 Barreto.
Subs not used: 25 Padelli, 9 De Vezze, 18 S.Masiello, 18 Greco, 30 Allegretti.
Coach: Giampiero Ventura.
Inter: 12 Julio Cesar; 13 Maicon, 6 Lucio, 25 Samuel (39 Santon 64), 2 Cordoba; 11 Muntari (7 Quaresma 65), 4 Zanetti; 45 Balotelli (19 Cambiasso 79), 10 Sneijder, 27 Pandev; 22 Milito.
Subs not used: 1 Toldo, 23 Materazzi, 44 Carlsen, 89 Arnautovic.
Coach: José Mourinho.
Referee: Roberto Rosetti (Turin).
Booked: Parisi 34, Samuel 59, Lucio 62, Bonucci 73, Belmonte 89.