Both teams have found wins hard to come by lately and this was a result that neither wanted.
The visitors created the better chances and the defeat of Inverness at home to Motherwell meant they eased two points clear of their relegation rivals.
However, the Hibernian fans made their own frustration clear as boos sounded around Easter Road at full-time, with the home side slipping further behind in the race for a top-six finish.
Paatelainen had to endure calls for his head after last weekend's 2-0 defeat to bottom club Inverness Caledonian Thistle, and the Finn responded by surprisingly making only two changes to the starting 11 he criticised so heavily in the Highlands.
Midfielders Denes Rosa and Ross Chisholm made way for Colin Nish and Joe Keenan in an attacking line-up which also featured Jonatan Johansson, Steven Fletcher and Derek Riordan.
But Hibs' attackers failed to find a goal and their record now shows just one win in their last 10 matches.
Hughes, Paatelainen's former Hibs team-mate, reacted to Falkirk's 2-1 defeat to Hamilton which left them only a point ahead of Inverness at the bottom by making four alterations.
Jackie McNamara and Neil McCann dropped out through injury, and Carl Finnigan and Dean Holden were relegated to the bench, with Lee Bullen, Tam Scobbie, Arnau Riera and Patrick Cregg being drafted in as the Bairns went in search of a first victory in 13 matches.
Paatelainen's stinging criticism of his players' lack of effort last weekend appeared to have the desired effect in the early stages as the home side chased every lost cause and competed for every loose ball.
Riordan, one of four strikers in the Hibs line-up, was particularly prominent as he made two block tackles as Falkirk tried to clear their lines.
In an error-strewn opening, it was predictably a mistake which gave Falkirk their first sight of the target three minutes later.
Hibernian captain Rob Jones and fellow defender Chris Hogg went for the same high ball but failed to deal with it, however goalkeeper Grzegorz Szamotulski was alert and held Steve Lovell's effort at the second attempt.
Riordan was again to the fore as Hibs launched a counter-attack thanks to a ball from Nish, but the man who started the move could not finish it as his attempt to bundle in Riordan's cross was blocked for a corner.
Falkirk enjoyed a period of sustained pressure around the half-hour mark, forcing a couple of corners and seeing Scott Arfield's free-kick blocked by Hibs' defensive wall.
Michael Higdon might have done better than head over from Scobbie's cross in the 37th minute and Szamotulski had to look lively as Bullen drove in.
It was Hibs who enjoyed the final chance of the half as Jones looped a header from Hogg's long free-kick onto the roof of the net.
The second period began in similar fashion to the first but Falkirk were first to threaten seven minutes after the restart.
Arfield sent in a wicked curling cross from the right which was just missed by Lovell and Higdon could not direct his lunging volley on target.
The big Bairns striker was more accurate five minutes later, however, as he struck the bar with a superb 25-yard drive, before Bullen drove horribly high and wide from eight yards out.
Paatelainen made two substitutions in quick succession, replacing Johansson and Keenan with Alan O'Brien and Rosa.
Hibs were keen to use the blistering pace of O'Brien at every opportunity but it was Falkirk's Burton O'Brien who almost broke the deadlock with 17 minutes remaining.
The former Livingston midfielder broke inside full-back Darren McCormack but Hogg got across to block his shot.
Arfield got a sight of goal in the 78th minute as he latched onto a loose ball on the edge of the box but sliced his drive wide of the target.
The youngster was then almost the architect of his side's downfall minutes later as he played a throw-in straight to Riordan after Hibs had played the ball out for a Falkirk injury.
Dani Mallo was forced to tip Rosa's chip over the bar.