Milan, Napoli, Siena into Italian Cup last eight
AC Milan's new Japanese midfielder Keisuke Honda reacts at the Mapei Arena stadium in Reggio Emilia, on January 12, 2014
Honda's goal helped Milan see off second tier La Spezia 3-1 while Callejon's double came in Napoli's 3-1 win over Atalanta.
Serie B side Siena stunned Catania 4-1 to also reach the last eight of the competition, in which Lazio, Roma, Udinese, Fiorentina and Juventus won their respective ties played previously.
Honda made his debut for Milan in Serie A last week when he came off the bench and came close to scoring in a 4-3 defeat to Sassuolo which prompted the sacking of coach Massimiliano Allegri.
Caretaker coach Mauro Tassotti was in charge Wednesday at the San Siro and gave Honda his first start although new coach, Dutchman Clarence Seedorf, arrived in time to see the second half of the game.
Brazilian Robinho opened the scoring for the hosts on 28 minutes, with striker Giampaolo Pazzini doubling the lead three minutes later.
Honda struck two minutes after the restart to all but wrap up the win, with Nicola Ferrari hitting a consolation for the visitors in second-half injury time.
Napoli were a class above Atalanta although there was controversy at the San Paolo, where Lorenzo Insigne's second goal was perhaps offside and protests from Atalanta led to the expulsion of veteran Colombian defender Mario Yepes.
Atalanta opened the scoring on 13 minutes thanks to a Giuseppe De Luca tap-in following a counter-attack, only for Callejon to level a minute later with a superb volley from a tight angle from Anthony Reveillere's cross.
Insigne, who had earlier smashed a free kick against the crossbar, put Napoli ahead in the 72nd minute in controversial circumstances.
Gonzalo Higuain was offside, but the intended pass for the Argentinian hit Atalanta defender Cristiano Del Grosso in the back.
Atalanta's defence stood still looking at the linesman but as they did so the ball bounced into Insigne's path and he turned the ball into the empty net.
Atalanta protested furiously, with Yepes going too far and earning a red card.
Callejon completed his brace shortly after when he sprung the offside trap to volley Gokhan Inler's ball past Ciro Polito.
Napoli will host Lazio in the quarters, Milan host Udinese. Fiorentina travel to second division Siena and Serie A champions and leaders Juventus, in the plum tie of the last eight, travel to second-placed Roma.