South Africa-born midfielder Keaghan Jacobs was making his fourth start of the season and sixth overall for Livingston.
The hosts took the lead in the 34th minute as Dolly Menga collected a cross from the flank before taking a touch and firing past Allan McGregor from close range.
Rangers went close to levelling matters just before the halftime break Ovie Ejaria - on loan from Liverpool - headed over the crossbar with only the goalkeeper to beat.
While Rangers struggled to carve out chances in the second half, Livingston went close to doubling their lead after the hour-mark but Scott Pittman saw his effort tipped away by McGregor.
Gerrard's men threw numbers forward in search of an equalising in the closing stages, but Livingston managed to see out the rest of the matches to claim three points.
As a result, Livingston have moved up to third place, while Rangers have dropped to sixth position.