The striker netted from a Garry Brady free-kick just before the hour, following a challenge on Gareth Wardlaw, to move Danny Lennon's side off the bottom of the table.
Hibs had had the better of the first half and twice came close through Derek Riordan free-kicks, but were unable to find an equaliser.
St Mirren and Hibs both made two changes to their starting line-ups.
Home manager Lennon welcomed back striker Wardlaw from injury and also started with Brady, who had played at Celtic the previous Sunday but missed the midweek penalty shootout defeat at Ross County in the Co-operative Insurance Cup.
Sean Lynch dropped to the St Mirren bench while Michael Higdon was missing from the squad.
John Hughes included Celtic target Anthony Stokes in his squad but the Hibs manager made two enforced changes - defender Steven Thicot came in to replace the injured Michael Hart and Colin Nish started in place of suspended Kevin McBride, sent off in last week's 3-0 defeat by Rangers.
Hibs won the first corner on four minutes and Riordan flighted in the delivery from the right, but Sol Bamba's commanding header went harmlessly wide of the far post.
St Mirren took a quick free-kick on 10 minutes after Bamba held back Wardlaw, Marc McAusland trying a speculative effort from the right touchline but Mark Brown clutched it easily at the opposite corner of his goal.
The visitors had another attempt on goal on the quarter-hour when Riordan's corner from the left ran right through the box and fell for Edwin de Graaf on the edge of the area, but his drive continued rising over the bar.
Riordan almost put his side in front as the first half reached its midway point. The forward curled a free-kick from just outside the left corner of the box past the five-man St Mirren wall but agonisingly just to the wrong side of the near post.
Paul McGowan launched a promising attack for the hosts on 28 minutes, taking possession on the halfway line and turning for goal before releasing Jure Travner on the left, but his cross was hooked clear by Bamba on the six-yard line.
Riordan again came close with another free-kick, this time further out than his earlier effort, but on this occasion his low drive to the bottom-right corner was beaten away by Paul Gallacher.
The home goalkeeper also punched away to safety a Riordan free-kick five minutes from the break.
Brady sent in a free-kick from the right after Hugh Murray was brought down but Lee Mair, arriving at pace in the six-yard box, was unable to connect, while Wardlaw headed onto the roof of the net a moment later.
De Graaf had the first effort of the second half, heading wide following good link-up play between Nish and Riordan.
Wardlaw was then floored twice in as many minutes by midfield challenges from Thicot and Chris Hogg. The Hibs players escaped bookings, but the St Mirren man found himself yellow-carded moments later for his challenge on Bamba as tempers frayed.
Bamba also escaped a booking for another heavy challenge on Wardlaw on 58 minutes.
However, the Paisley side responded in style from the free-kick, when Brady's ball in from the right touchline was flicked on through the box by Darren McGregor to Dargo, who slotted into the bottom-left corner.
Gallacher comfortably caught another Riordan corner in a busy box eight minutes later as the visitors attempted to restore parity.
Liam Miller hit a cross onto the roof of the net as the game entered its final quarter, while Darren McGregor came close with a downward header from Brady's free-kick which sneaked wide.
McGowan then tried his luck with a rising effort from outside the box, but it was easily claimed by goalkeeper Brown, as was a promising cross from the left by substitute Sean Lynch.
Hibs had plenty of possession in and around the opposing penalty area in the closing minutes, but were met by stout defending and were unable to make the breakthrough.