Simeone, the son of former Lazio player and long-time Atletico Madrid coach Diego, struck twice in each half to sink Maurizio Sarri's Lazio, who briefly threatened when Ciro Immobile halved the deficit seconds after the break.
Verona move up to 11th on 11 points after starting the day hovering above the drop zone, while Lazio drop to eighth, a point behind city rivals Roma who are fourth ahead of their clash with league leaders Napoli later on Sunday.
Sarri had selected the great-grandson of Italian dictator Benito Mussolini in his squad for the match, but did not play him.
Defender Romano Floriani Mussolini, 18, came through the youth ranks at the club after previously playing for their local rivals Roma.
Fiorentina meanwhile are sixth, level on points with Roma, after recovering from two painful recent defeats with their hammering of Cagliari.
Vincenzo Italiano's side had lost their last two matches against league leaders Napoli and promoted Venezia, with the latter provoking fierce protests from fans which targeted striker Dusan Vlahovic.
The fans at the Stadio Artemio Franchi in Florence whistled their star forward before Sunday's match, the Serb guilty of not renewing his contract which is set to expire at the end of next season.
Vlahovic, 21, refused to take the 21st-minute penalty which captain Cristiano Biraghi scored to put the hosts ahead.
However he did score his team's third four minutes after the break following Nicolas Gonzalez's strike which doubled their lead three minutes before half-time.
Sunday ends with champions Inter Milan facing fierce rivals Juventus in what is traditionally one of the biggest matches of the season. (AFP)

D’Tigress begin US tour with historic Sparks clash
Tinubu congratulates basketball star Anosike on NBL title, MVP award in China
NSC announces UK trials for diaspora athletes
Adams calls for urgent reset in Nigerian football
Playing for Nigeria felt like playing for Real Madrid – Arokodare
Playing for Nigeria felt like playing for Real Madrid – Arokodare
NFF opens talks with Osula over Eagles switch
Brume, Okezie join global stars for Kip Keino Classic
NPFL confirms May 24 season end date
NCF proposes elite cricket league
Trump envoy wants Italy to replace Iran at World Cup — Report
Gala intensify Osimhen’s special recovery plan
Rangers International going, going . . . (63,728 views)
Amaju Pinnick: A cat with nine lives (55,051 views)
Second Term: Amaju Pinnick, Other NFF Heavyweights Home to Roost •How Pinnick Broke the Jinx (52,984 views)
Current issues in Nigerian sports: Matters arising (52,575 views)
Sports Development: Zenith Bank on the zenith (52,504 views)
Missing $150,000 IAAF Grant: Solomon Dalung’s Hide and Seek game (52,403 views)
Gov. Abdullahi Ganduje’s solid footprints, commitment to sports development in Kano State (52,254 views)
NFF Presidency: Pinnick, Maigari, Ogunjobi, Okoye in Battle for Supremacy (51,800 views)
Olopade, BET9A wave of revolution in NNL (50,988 views)
Commonwealth Games 2018: Shame of Muhammadu Buhari, Solomon Dalung (49,497 views)
Ibrahimovic’s Man U exit: Whose decision is it? And in whose interest? (47,914 views)
John Mikel Obi: Segun Odegbami’s Outrageous Call! (47,375 views)