The Serie A side was not at its best at Ludogorets Arena but scored the opener from the best move of the match, Eriksen curling home from the edge of the box.
January signing Eriksen hit the crossbar from distance and Romelu Lukaku's late penalty confirmed a victory for the Nerazzurri that saw them bounce back from successive domestic defeats.
Inter, which began with Lukaku on the bench, struggled to impose itself in the opening exchanges but Ludogorets goalkeeper Plamen Iliev had to make a smart stop to keep out Cristiano Biraghi's volley in the 25th minute.
The upright kept out Alexis Sanchez's clever flick after the restart, then Lautaro Martinez lashed a long-range strike narrowly over the crossbar as Inter increased the tempo.
Iliev made another fine save to turn away Eriksen's bouncing 20-yard volley, but the goalkeeper could do nothing about Inter's first goal in the 71st minute.
Sanchez and substitute Lukaku were involved in patient passing in the build-up, with Eriksen sweeping an excellent finish out of Iliev's reach.
It was almost 2-0 moments later as Eriksen's thumping drive beat Iliev but not the woodwork, Lukaku's arrival having given Ludogorets more to think about in defence.
Ludogorets, who were without their star striker Claudiu Keseru due to injury, failed to record a shot on target and face an uphill battle at San Siro next week after Lukaku converted from 12 yards in added time following Anicet Andrianantenaina's handball.