Napoli closed the gap on second-placed Roma to just two points with victory over Sampdoria, while Kaka scored his 100th goal for AC Milan as they saw off Atalanta and Edy Reja picked up his first win in his first game for Lazio.
With Roma losing 3-0 to leaders Juventus on Sunday, Rafa Benitez’s side had the chance to edge themselves closer to the capital club.
And thanks to a second-half brace from Dries Mertens, Napoli ran out 2-0 winners against Sampdoria, although they still remain 10 points adrift of Juve.
The Partenopei were made to work hard by their opponents, who were twice denied by the woodwork in the second half.
Kaka struck twice for AC Milan as the Rossoneri secured a confidence-building 3-0 win over Atalanta at the San Siro.
It has so far been a troubled season at the San Siro with coach Massimiliano Allegri confirming last week that this season will be his last at the helm.
But two goals from Kaka and a third from Bryan Cristante gave Milan the perfect start to 2014 with a comfortable victory.
The win was just Milan's second league victory in their last 10 games and moved them up to 10th, while Atalanta remain in 15th.
Miroslav Klose's late winner against Inter Milan gave Edy Reja a successful start to his second spell in charge of Lazio.
The German forward struck nine minutes from time to hand Lazio a deserved 1-0 victory in their first game of 2014. Lazio, who had won just one of their last eight league matches heading into the contest, decided to sack Vladimir Petkovic at the weekend. The victory has lifted the Romans to 10th place while it has left Inter in sixth, eight points behind third-top Napoli.
Udinese's struggles look to have carried over into the second half of the Serie A season as they ended the winter break with a 3-1 home defeat to a Hellas Verona side who had previously won just once away from home in this campaign.
In the build-up to the match Udinese captain Antonio Di Natale had said coach Francesco Guidolin could remain calm as the players had the quality to turn their campaign around. But Guidolin was far from relaxed as he was sent to the stands for dissent before half-time with his team slumping to a 10th defeat of the season.
Luca Toni scored twice in the first half to put Verona on top and although Roberto Pereyra got one back before the break, Guidolin's emotions boiled over, with his mood hardly improved by Juan Iturbe's third for Verona 20 minutes from time.
Parma came from behind to begin 2014 with their first win in six weeks, ending the winning streak of a Torino side hoping to push for a European place in the second half of the season.
Torino ended last year by winning three in a row to move up to seventh in Serie A, and they were off to a flyer when Antonio Mirante put them 1-0 up after 21 minutes.
But Marco Marchionni levelled before Alessandro Lucarelli put Parma ahead on the stroke of half-time, with Amauri wrapping up a 3-1 win 20 minutes from time.
Genoa halted a five-match winless run with a comfortable 2-0 victory over Sassuolo on Monday afternoon.
Alberto Gilardino set Genoa on their way in the 28th minute from the penalty spot, before Alberto Bertolacci made it two before the interval.
Gilardino could have scored his second of the afternoon two minutes from time but saw another penalty superbly saved by Sassuolo goalkeeper Gianluca Pegolo.
The outcome was Genoa's first win since Nov. 10 and lifted the Grifoni to ninth in Serie A.
Francesco Lodi marked his return to Catania with a match-winning display against Bologna on Monday afternoon.
The Italian midfielder set up Gonzalo Bergessio for Catania's opener in the 23rd minute and then converted his team's second from the penalty spot after the hour mark.
The 2-0 outcome in Sicily handed Serie A's bottom club a perfect start to 2014 and their first win since Nov. 9.
Bologna, who struggled without suspended playmaker Alessandro Diamanti, slipped to their third defeat in four games and have dropped to 17th place, one point clear of the drop zone.
Information from the Press Association was used in this report