Roberto Mancini's side went into Sunday's game having picked up just one win from their last five league matches on home soil.
With Lazio coming off a hat-trick of victories in all competitions, it always looked likely to be a tricky test for the hosts.
Felipe Anderson's quickfire opener hardly did Inter's fragile confidence any favours, with the in-form Brazilian maintaining his hot streak after netting in two of those recent triumphs.
Mancini's head was in his hands as the 21-year-old striker doubled the advantage before the break with a second clinical finish.
However, Mateo Kovacic raised hopes of a recovery with a stunning strike just after the hour mark and Rodrigo Palacio claimed a poacher's goal to level 10 minutes from time.
Inter made just one change from last Monday's 2-0 win at Chievo, with Brazilian defender Dodo coming in for Chile international Gary Medel.
After beating Atalanta 3-0 at home eight days ago, Lazio replaced Alvaro Gonzalez and Filip Djordjevic with Miroslav Klose and Marco Parolo.
The visitors stormed into the lead after just two minutes when Stefan Radu whipped in a cross which Anderson controlled superbly before firing past Samir Handanovic.
Anderson could have had another just four minutes later but volleyed over the bar, while Federico Marchetti got down well to save a long-range Fredy Guarin effort at the other end.
Another well-struck Guarin shot flew just wide from 25 yards out soon after the half-hour mark, but it was Lazio who hit the target again next eight minutes before the break.
Loose play from Andrea Ranocchia allowed the away side to counter-attack as Klose's headed flick-on found Anderson, who cut in from the left past some flimsy tackling before wrong-footing the goalkeeper with a low shot.
Medel was introduced at the expense of Dodo just before the break and Inter tried to rally after the interval by getting more men and a number of crosses into the box.
Mauro Icardi should have done better after being set up by Kovacic and Marchetti had to dive at full stretch to keep out a deflected Zdravko Kuzmanovic effort.
However, Marchetti could not stop Kovacic's thunderous volley from the edge of the area hitting the back of the net after Lazio failed to sufficiently clear a 66th-minute corner.
That strike lifted the home crowd, who went wild 14 minutes later when Palacio pounced on a Danilo D'Ambrosio nod down from substitute Federico Bonazzoli's free-kick.