Even the loss of top scorer Kane Hemmings to injury after just 13 minutes could not prevent Jimmy Nicholl's side from taking all three points as on-loan Rory McKeown announced his arrival from Kilmarnock with the opening goal, a well-placed strike after 33 minutes.
Dundee threw everything at the home side in the second half but Greg Stewart sealed the points by providing a sucker-punch on the break with just nine minutes remaining.
The result leaves Dundee just a point clear of Hamilton, who beat Livingston on Friday, while Falkirk kept in touch with a narrow 1-0 home win over Queen of the South.
The Bairns claimed all three points at home thanks to a penalty strike from midfielder Mark Millar.
The home side were dominant for most of the first half, their best chance falling to on-loan Carlisle United striker Mark Beck, whose 34th-minute shot was well saved by Queens goalkeeper Zander Clark.
Queen of the South rallied after the interval, with Falkirk keeper Michael McGovern saving well firstly from a Paul Burns volley and then from an Iain Russell 20 yarder, but Millar's late penalty, awarded after a handball offence by Chris Mitchell, gave Gary Holt's men a crucial victory.
Dumbarton and Raith Rovers served up a thrilling 3-3 draw at Bet Butler Stadium.
Colin Nish drew first blood with an emphatic finish into the top corner after Lee Robinson had denied Chris Kane but Raith equalised shortly afterwards when Gordon Smith found the net after John Baird took advantage of a mistake by Dumbarton defender Scott Linton.
Kane put Dumbarton back in front eight minutes from half-time with a well-taken goal but Baird equalised in the 57th minute after Smith's shot had come back off the post.
Smith then headed Raith in front but Scott Agnew equalised for Dumbarton with a breathtaking volley from just outside the area.
Morton lost for the first time in six matches, going down 1-0 to Alloa Athletic at Cappielow.
Nothing much went right for the home side and they were up against it from the moment Ryan McCord beat the offside trap to net what turned out to be the only goal after 18 minutes.
Archie Campbell had a chance to equalise for Morton just before half-time when he shot over from Garry O'Connor's lay-off.
O'Connor came even closer shortly afterwards as his shot slipped inches past the post.
Scott Bain then made a fine save in the second half to deny Rowan Vine and add to the frustrations of the home fans.
Derek Riordan was introduced for the final 12 minutes in the hope that he could unlock the Alloa defence but they stood firm.
To complete a miserable day for the home side - who are now a dozen points adrift at the foot of the table - Dougie Imrie was sent off in the final minute for a professional foul.