Chiukepo registered his name on the scoresheet 15 minutes from half time break.
It was enough for the Blantyre based side, widely known as the People's Team, to pocket three points.
Despite bagging maximum points over the military, Bullets are still on the log table with 34 points from 17 games while Red Lions, perched on position 10, have 20 points from 18 games.
Both sides a created a number of scoring opportunities in the first half, but failed to hit the back of the net.The first half ended goalless.
Chiukepo punished the host in the 60th minute when he headed home after Red Lions failed to tame Mussa Manyenje's well-curved cross from the left flank.
This was Red Lions' third defeat to Bullets. The soldiers lost in the first round of the league and also in the Carlsberg Cup, which Bullets won after beating their city rivals Mighty Be Forward Wanderers.
Coach for Red Lions Pritchard Mwanza conceded defeat and indicated that they will polish up areas identified to have failed them.
"It’s painful to lose to Bullets once more. My boys tried to come back into the game, but missed the target. We are able to create chances, but unable to score," said Mwanza.
Bullets Team Manager James Chilapondwa hailed the players for the gallant fight.
"It was a hard game, they were equally determined, but we thank God that we have collected the points and we look forward to collecting more points in our next assignments," said Chilapondwa.
Elsewhere, Dwangwa United restricted Azam Tigers to a barren draw at MDC Ground while Mzuni FC and Civil Sportig pocketed a point each after settling for a 1-all draw at Civo Stadium in Lilongwe.
Fletcher Bandawe netted for the home side while Chisomo Gillioni scored for Mzuni.