Daly netted twice in the second half to help the Gers defeat Airdrieonians by a 3-0 scoreline and progress to the fourth round of the national cup competition.
Having bagged a hat-trick in the 4-0 win over East Fife last Saturday and scored the winning goal against Stenhousemuir on Tuesday, the double rounded off a good seven days.
The Irishman's highly-impressive contribution also kept alive his club's hopes of winning a domestic treble in the 2013/14 campaign.
The Glasgow giants are running away with SPFL League One and will also play in the final of the Ramsdens Cup against Raith Rovers next April.
The 30-year-old's brace sent him further ahead at the top of the scoring charts in the third tier; he has now been on target 14 times in all competitions.
Rangers midfield lynchpin Ian Black was suspended for this game having been sent off in the Ibrox club's last Scottish Cup game against Dundee United last season.
Kyle Hutton, who has been unable to win a first-team start since recovering from ankle ligament damage, was drafted in to replace the former Hearts man.
He was the only change to the side that had beaten Stenhousemuir 1-0 in the semi-final of the Ramsdens Cup at Ochilview on Tuesday evening.
And there was a warm round of applause for former Rangers player Fernando Ricksen, who has been diagnosed with Motor Neurone Disease, before kick-off.
There was also a minute's applause from both sets of fans for Ricksen in the second minute of the game. The Dutchman wore the No.2 jersey during his time in Glasgow.
Veteran goalkeeper Tony Bullock started in goal for the visitors - Scott Gallacher was not able to play - after being signed as emergency cover for this match.
Lee McCulloch nearly turned the ball into his own net in the ninth minute when he miscued an attempted clearance from a Jamie Bain cross. Fortunately for the Light Blues captain, Cammy Bell safely gathered the ball to spare his blushes and keep the home team on level terms.
On the last occasion these two teams met - in an SPFL League One match at the Excelsior Stadium back in August - the Glasgow club ran out emphatic 6-0 winners.
But since then there has been a change of manager at the Lanarkshire club, with former Rangers player Gary Bollan replacing Jimmy Boyle last month.
The Diamonds adopted an ultra-defensive formation - at times they had six or seven players strung across their defence - and successfully frustrated their rivals.
Bilel Mohsni was probably the brightest of the home team's players in the first half, with the opposing team struggled to deal with the defender's powerful runs upfield.
Still, the French-Tunisian centre-half was unable to carve out any openings which strikers Nicky Clark and Jon Daly could successfully exploit.
Nicky Law, a deserved man of the match in midweek, also performed well and was only prevented from netting by some excellent defending from Darren McCormack and Grant Drummond.
Rangers came close to breaking the deadlock just before half-time after Arnold Peralta was hauled down by Pat Boyle out on the right wing.
The Honduran played the free-kick into the Airdrie box and McCulloch met it with a downward header. However, he only succeeded in hitting the side netting.
With the news that Dave King was not, for the time being at least, going to invest in the club, there had been predictions of widespread protests. There were a few anti-board banners in the stands - including one that read "No More Faceless Investors" - but the crowd seemed more concerned with getting behind the players.
Their backing paid off when Ally McCoist's side took the lead four minutes into the second half after another fine delivery from Peralta on the right wing.
Clark nodded the ball on to Daly, who controlled it with the outside of his foot before curling it beyond the clutches of Bullock and into the bottom right corner of goal.
The former Dundee United striker, who won the Scottish Cup with the Tannadice club back in 2010, added another goal just three minutes later. Ricky Foster lofted a cross into the Airdrie box from wide on the right and Daly, diving in to make sure he connected, did brilliantly to head the ball into the net.
Lewis Macleod, who had put in a tireless shift all night out on the left side of midfield, made way for his team-mate David Templeton in the 66th minute.
With his side's safe progress to the next round of the competition looking increasingly likely, McCoist replaced Clark with Andy Little in the 70th minute of the match.
Bollan, meanwhile, threw on Liam Watt for Lewis Coult in an attempt to drag his team back into the game. But his charges were clearly tiring.
But there was still time for McCoist's men to add another goal to their tally when Templeton grabbed the third in the 80th minute.
So, Rangers move safely into the fourth round, and they will be hoping Sir Alex Ferguson will give them another home tie when he helps to make the draw in Aberdeen next Tuesday.