Fiorentina knocks off Bologna
Josip Ilicic, Borja Valero and Giuseppe Rossi were on target for the Viola, who went into Sunday's match on the back of Thursday's 2-1 triumph over Dnipro that allowed Vincenzo Montella's side to secure top spot in Europa League Group E.
The result leaves Stefano Pioli's side in 19th place in the league and without a win in all competitions since October.
Klose's goals came in the space of seven minutes as he first profited on a Antonio Candreva assist before the Livorno defense was compliant in allowing him to effectively kill off the game inside half and hour.
The veteran Germany striker, who had just two league goals coming into the game, could have had a hat-trick too after he had hit a post shortly before opening the scoring.
Lazio had not tasted league success since they beat Cagliari 2-0 seven games ago - the last time Klose had scored - although Livorno have now taken just a single point in five games to drop them into the relegation places.
Eder's first-half header was enough to earn Samp all three points and extend their unbeaten run to five matches in all competitions.
The defeat brought an end to a four-match winning run for Eugenio Corini's Chievo, who remain just above the relegation zone.
In a match with plenty of chances but no goals, Cagliari had their fair share of opportunities to end a winless away run which dates back to February 17.
The result extends Parma's unbeaten league run to five matches, but if Roberto Donadoni felt his side threw away two points in their 3-3 draw with Inter Milan last time out, he may well feel the same about this one given the number of openings they had after the break.
Genoa looked set to extend their strong recent home run after Andrea Bertolacci slotted home in the 72nd minute but Atalanta belied their own dismal recent away form by popping up with the equalizer to make it 1-1 four minutes into time added on.
It was well deserved for the visitors, who had the bulk of the chances in the match despite Genoa starting the stronger.
Second-half goals from Alexander Farnerud and Ciro Immobile proved the difference as Torino climbed to seventh in Serie A on the back of their third win in four games.
For Udinese the picture is far more bleak, with Sunday's result meaning they have now won just one of their last six league games and drop to 15th in the standings, four points above the relegation zone.