Lazio took to the field wearing a "No Racism" logo on their shirts in the aftermath of an attack in Rome on Tottenham Hotspur fans on the eve of last week's Europa League tie and anti-Semitic chanting during the game with the London team.
However, chants of "Roma, Jewish club" could be heard on Tuesday from the Curva Nord, home to Lazio's hardline ultra supporters, aimed at their bitter local rivals, although other sections of the crowd booed and tried to drown them out.
UEFA is deciding what sanctions to take after the events of last week, with Lazio president Claudio Lotito having met one of the injured Spurs fans, many of whom are Jewish, in hospital earlier on Tuesday.
The victory over Udinese took fifth-placed Lazio to 26 points from 14 games, six behind leaders Juventus and within two of Fiorentina and Inter Milan in third and fourth respectively.
Lazio started brightly, earning a penalty in the 11th minute when Udinese's Willians handled as he got in the way of Stefan Radu's backheel from a corner.
However, Antonio Candreva's spot kick was weak, allowing visiting goalkeeper Zeljko Brkic to save.
Five minutes later Lazio did take the lead when the lively Stefano Mauri's nicely-weighted pass found Gonzalez, who slotted the ball past Udinese's Serbian keeper.
With playmaker Candreva, on loan from Udinese, working well in a wider role and Mauri and Ederson controlling central midfield, Lazio were in control for long stretches of the game.
It was thus no great surprise when they scored a second just past the half-hour thanks to another Mauri assist which found Klose, who beat the offside trap before coolly side-footing home.
The victory was secured shortly just before the hour when Brazilian Hernanes, a halftime substitute for Ederson, clipped a free kick, awarded for a clumsy Andrea Coda challenge on Klose, over the wall and into the net from the edge of the box.
"That was a great performance," Lazio's Bosnian coach Vladimir Petkovic told Sky Italia.
"It wasn't easy after the missed penalty, but we believed in ourselves, we kept up a high rhythm for 90 minutes and didn't allow Udinese any space.
Udinese coach Francesco Guidolin, whose side finished fourth last season but are currently languishing in 12th after five games without a win, said they now had lots of work to do.
"We've got to start again, because if we carry on like this we're not going to be going anywhere. This can't be the real Udinese. Yes, we've got problems with injuries, but that's no excuse. Our objective now has to be to reach 40 points."