Dickoh struck from close range following Callum Booth's 87th-minute corner to leave St Mirren firmly in the relegation equation.
Hibs midfielder Martin Scott had twice headed against the woodwork but there was little between the teams in a scrappy encounter.
The game appeared to be drifting to a goalless draw but the late drama gives Hibs a huge cushion over Accies, who have not won since October, while St Mirren remain five points above the Lanarkshire side.
Hibernian had leapfrogged St Mirren in the table with a 2-0 triumph at Easter Road earlier this month, before following it up with victory over Kilmarnock.
St Mirren, who matched Hibernian's 4-4-2 formation, were determined to atone for that below-par performance and they started well with Jim Goodwin flicking Paul McGowan's corner wide.
Booth's misjudgement allowed McGowan a brief sight of goal but the angle was too tight to shoot and Paul Hanlon prevented Hugh Murray from finishing his cutback.
McGowan soon set up another opening when his cross was headed down by Michael Higdon but Craig Dargo just failed to connect.
Hibernian, who were without the suspended Ian Murray, created their first chance in the 13th minute when Scott headed off the post following a David Wotherspoon cross, and Akpo Sodje shot over on the turn seconds later.
Derek Riordan volleyed a difficult chance just over from 20 yards but St Mirren came back into it and Graham Stack did well to hold McGowan's left-footed strike from the edge of the box.
The half continued in a scrappy fashion amid windy conditions with Hanlon defending well for Hibs as St Mirren tried to exert pressure.
Scott hit the woodwork again in injury-time after Sodje's flick-on but Paul Gallacher had his looping header covered as it hit off the top of the bar.
Stack took no chances with Jure Travner's inswinging free-kick, diving to punch the ball away as it swirled in the wind.
But the second period was proving even more scrappy, although Riordan produced a much-needed moment of quality when he took a return pass from Scott and blasted a powerful strike from 20 yards which Gallacher fumbled wide.
McGowan continued to provide the class for St Mirren, his well-timed pass allowing Dargo a chance on the counter-attack but the striker's attempted chip cleared the crossbar.
Dargo almost broke the stalemate with a clever through ball for Higdon but the striker was flagged offside in what was a marginal decision, although Stack was quickly off his line.
Another opening soon appeared for Saints but McGowan's touch for once let him down as he ran on to Hugh Murray's pass.
Colin Nish replaced Sodje and soon saw a deflected volley flash wide, with the corner producing a better chance.
Booth's delivery fell for Dickoh, whose powerful low strike from 10 yards was blocked by the diving Gallacher.
But Gallacher was beaten moments later. Left-back Booth's deep delivery was headed back in by Hanlon and his centre-back partner headed it in from underneath the bar.