Inter recovered from a goal down to beat Ludogorets 2-1 at an empty San Siro and seal a 4-1 aggregate victory in Friday's (AEDT) Europa League last-32 tie.
Antonio Conte's men took a two-goal lead into the second leg, which was played behind closed doors due to concerns over the coronavirus outbreak in Italy.
Cauly profited from some sloppy defending to halve the deficit with 26 minutes played, but Cristiano Biraghi squeezed in a deflected effort from an angle after being played in by Christian Eriksen to level things up on the night.
Romelu Lukaku edged the Italian club ahead with a strange goal just before half-time and competition favourites Inter saw things through to book a place in Friday's last-16 draw.
Lukaku, who had also scored a late penalty in last week's first leg after Eriksen's opener, failed to beat Plamen Iliev from a one-on-one five minutes into this return match.
Bulgarian champions Ludogorets gave themselves some hope when Cauly held off Diego Godin and fired past Daniele Padelli at his neat post via the underside of the crossbar.
But Inter restored their two-goal aggregate margin 188 seconds later as Biraghi's drilled effort from the left went in via a deflection off visiting defender Georgi Terziev.
Lukaku then atoned for his earlier miss by scoring a bizarre fourth goal of the tie for Inter, with the ball ricocheting off his body while on the floor after his initial header was saved.
Alexis Sanchez played a big part in that goal and struck the frame of the goal with a 25-yard drive early in the second half.
Lukaku was also denied by a mixture of Iliev and the post five minutes later but, a near-miss from substitute Mavis Tchibota aside, Inter had little trouble in seeing out a second victory on the bounce ahead of Sunday's trip to Juventus.
What does it mean? Inter regain some momentum
Successive wins against Ludogorets, either side of Sunday's postponed league clash with Sampdoria, has given Inter some much-needed momentum after back-to-back losses.
This weekend's trip to Juventus has officially been given the go ahead and Conte's men know that defeat in Turin could kill off their Scudetto title hopes, making it a truly huge game.
Lukaku's fine form continues
Lukaku's goal may have been fortunate, but he linked up well with Sanchez in the build-up and now has 23 for the season in all competitions.
The Belgium international joins Samuel Eto'o as the only Inter players to have scored at least two goals in four different competitions in a single season, excluding qualifiers.
Calamity defending for Ludogorets' opener
Godin claimed he was shoved off the ball by Cauly for the visitors' goal, but the VAR officials agreed with the referee's assessment and let it stand.
Not only was the veteran centre-back caught out, captain Andrea Ranocchia also failed to close down the Ludogorets goal-scorer and Padelli was easily beaten at his near post.
Inter travel to Serie A leaders Juventus on Sunday in another behind-closed-doors match, while Ludogorets head to Arda the same day as they close in on a ninth successive Bulgarian First League title.