The Nerazzurri dropped down to fourth place by virtue of Roma's win over Udinese earlier in the day, but they failed to respond in kind and build on their victory over Bologna last weekend, which is now their only triumph in their last 10 matches.
The hosts almost took the lead in unorthodox fashion after only eight minutes when Pandev's long ball forward eluded everyone before bouncing up against the crossbar and landing kindly in the arms of a grateful Samir Handanovic.
Inter's best chance of the first half fell the way of youngster Yann Karamoh after 19 minutes, but he could not follow up his winner last weekend with another goal as he sliced his volley off target from a promising position.
Antonio Candreva was the next to come close for the visitors when he fired a fine shot towards goal from the corner of the area, but Mattia Perin was at full stretch in the Genoa goal to parry the effort away.
It was the home side who went into the break ahead, though, with Inter seeing luck desert them right on the stroke of half time when Milan Skriniar's clearance from an Ervin Zukanovic cross slammed straight into an unwitting Ranocchia and deflected past Handanovic for the opening goal.
Inter have not won an away game since November, and their attempts to end that long wait were made all the more difficult when Genoa doubled their advantage just before the hour mark.
Diego Laxalt dragged an effort from the edge of the box, but that merely turned it into a good pass for Pandev, who reacted well to control it and then slide his finish past Handanovic from inside the area.
Candreva looked the most likely to give Inter a route back into the match, but he saw another long-range effort denied by Perin as Genoa held on to their lead.
The visitors did create a late chance to pull a goal back and perhaps set up a grandstand finale when Danilo D'Ambrosio collected a cross at the back post, but his low drive was kept out by Perin in stoppage time.
Genoa successfully hung on to their clean sheet and all three points, lifting them now 13 points clear of the relegation zone while Inter are in danger of dropping out of the Champions League places this weekend should Lazio beat Verona on Monday night.
GENOA (3-5-2): Perin; Rossettini, Spolli, Zukanovic; Rosi, Bessa (Omeonga, 56'), Bertolacci, Hiljemark, Laxalt; Pandev (Lazovic, 80'), Galabinov (Lapadula, 77')
INTER MILAN (4-2-3-1): Handanovic; Cancelo, Ranocchia, Skriniar, D'Ambrosio; Vecino (Rafinha, 62'), Gagliardini, Karamoh, Valero (Brozovic, 76'), Candreva (Pinamonti, 77'); Martins