Following a goalless first half, the defender got the last touch in a goalmouth scramble in the 62nd minute before heading in his second 13 minutes from time from close range.
Hibs, who had been buoyed by the Boxing Day win at rival Hearts, lacked creativity throughout the 90 minutes.
It was clear from the first minute that the swirling wind at the Tony Macaroni Arena was going to cause havoc.
It was route-one football that conjured up the first chance for the visitors after six minutes.
There was brief panic in the Hibs rearguard in the 17th minute, too, after Darren McGregor allowed himself to be dispossessed by Lyndon Dykes but the Australian's left-footed strike from 20 yards was partially blocked by the defender before Marciano gathered.
Hibs created their best chance of the half in the 38th minute when Doidge worked a one-two with Daryl Horgan before firing a left-footed strike over the bar from 18 yards.
There was still time for Livingston midfielder Jacobs to lift a shot over the bar before the half was over after connecting first time with Lawson's cut-back.
The Lions kept up the pressure with a series of corners and finally made one count just after the hour mark.
Sibbald's dangerous delivery led to a scramble and Guthrie got the final touch to open the scoring.
The points were sealed in the 77th minute when Guthrie notched his second, heading Lawson's delivery into the net from close range to take his tally to four in five games.
Livingston came close to a third but Hibs defender McGregor made a timely interception with Dykes ready to connect with Scott Pittman's pass.