Ionita volleyed over from a good position before Christodoulopoulos hit the underside of the crossbar with the ball bouncing down onto the line and out to safety.
Toni pulled a shot just wide with Inter hanging on for their lives, but with only a minute left to resist, they were beaten by Lopez, who turned up the heat on Mazzarri in front of watching club president Erick Thohir.
In Sunday’s other matches, Empoli snapped a three-game losing streak to inflict Lazio’s first defeat in seven matches with a 2-1 win at the Stadio Castellini.
Federico Barba put the Tuscan side in front on the hour mark, with Massimo Maccarone doubling their lead soon after.
Filip Djordjevic pulled a goal back for the Biancocelesti but they were unable to find an equalizer as they missed an opportunity to move level with Roma in second.
Paulo Dybala scored one penalty and missed another as Palermo dominated a 1-1 draw with Udinese at the Stadio Renzo Barbera.
The in-form Argentinian striker cancelled out Cyril Thereau’s early opener from the spot just before the break and worked hardest in the pursuit of a winning goal for the Sicilians.
Visiting goalkeeper Orestis Karnezis thwarted him at nearly every turn, however, most importantly repelling his second spot-kick in the 53rd minute.
Sergio Pellissier was Chievo’s hero as his first two goals of the season lifted them off the foot of Serie A and above their opponents Cesena after a 2-1 win.
Ten-man Genoa missed an opportunity to win four consecutive top-flight games for the first time since 2009 and were lucky to take a point from a 1-1 draw at Cagliari.