The Argentina international grabbed a point for the visitors after Francesco Totti's contentious spot kick gave Zdenek Zeman's team a deserved lead in a match it should have won.
Francesco Totti's controversial penalty was all the home side had to show for its dominance and the supporters were again left to dwell on match where the club failed to hold onto a lead.
Despite securing a draw, Inter is now nine points behind Serie A leader Juventus in fourth while Roma sits seventh, a further six points behind.
Zdenek Zeman set his team up in his favorite 4-3-3 formation, and it was unsurprisingly on the attack early, with Pablo Osvaldo just failing to meet Erik Lamela's searching cross before Alessandro Florenzi fired over from the edge of the area.
After a frenetic opening, the match settled down until the 20th minute when Michael Bradley broke into the box and was adjudged to have been brought down by Andrea Ranocchia, though replays showed the contact between the two was minimal.
Talisman Totti stepped up and emphatically sent Samir Handanovic the wrong way from 12 yards to give the home side the lead.
The Giallorossi were dominant in all areas of the pitch, and Florenzi almost doubled their lead when he volleyed just wide after a cross was only cleared to the edge of the area.
Roma was by far the superior outfit and Lamela was the next to go close but his curling effort sailed just wide of the post while Fredy Guarin's powerful effort flew just over the bar at the other end.
Serie A debutant Marko Livaja had a quiet opening to his first start of the league season for the visitors, but he almost set the Stadio Olimpico alight with a half volley that struck the post with Mauro Goicoechea helpless before Osvaldo twice fired wide when well placed.
Andrea Stramaccioni's side finally had the bit between its teeth and grabbed an equalizer on the verge of halftime as Guarin powered his way to the line before laying the ball across for Palacio to tap in.
A superb through ball from Lamela set Osvaldo free early in the second period but his heavy touch allowed Handanovic to claim the ball at his feet, and the goalkeeper did well to deny Totti from the follow up.
Zeman's team continued its good start to the second half and Ivan Piris tested Handanovic from distance, but his shot was straight at the Slovenia international.
With the game entering the final 20 minutes, Livaja again went close to marking his first league start with a goal, only to pull his shot from the edge of the area wide with the aid of a deflection.
Right back Piris was providing a good outlet in attacking positions, but the defender wasted two good chances as he failed to hit the target on both occasions.
Roma continued the search for a winner and Lamela forced Handanovic into the best save of the match as he did well to parry a low effort round the post.
The home side continued to push for a winner but couldn't find the killer pass and was left to settle for a point.