On this occasion St. Mirren made the most of home advantage and at times caused Rangers a lot of problems with Gus MacPherson sticking with the 3-5-2 formation, and the same players, that beat Hearts on Tuesday night.
In the second-half, in particular, the Buddies could have taken the lead with Bougherra twice having to clear the ball off the line to deny Michael Higdon.
Full credit, however, must go to young Danny Wilson who threw himself in to every challenge and coped well with another physical challenge from the Higdon-Mehmet partnership.
Rangers were not at their best this afternoon but they stuck to their task and came up against a side clearly buoyed after reaching the League Cup final.
Even the introduction of Kenny Miller and Kris Boyd on the hour mark could not change the game and the Saints fans applauded their team’s efforts after the final whistle.
Rangers welcomed back Madjid Bougherra in to the team while Steven Naismith made his first start since November 28 alongside Kyle Lafferty.
In total Walter Smith has made four changes to his line-up that beat St. Johnstone at Hampden on Wednesday night.
In goals Allan McGregor replaced Neil Alexander and the club’s no. 1 was protected by a back four consisting of Kirk Broadfoot, Bougherra, Danny Wilson and Stevie Smith.
Broadfoot’s inclusion meant that Steven Whittaker moved to the left side of midfield with Steven Davis on the right and Kevin Thomson and Lee McCulloch through the middle.
On the bench Nacho Novo, Andrew Little and Neil Alexander joined Miller and Boyd.
Rangers started the tie positively and after just one minute they had the first chance of the game.
Steven Davis probed down the right but turned back and passed the ball in to the path of Bougherra.
The Algerian’s cross was decent but McCulloch headed over from 15 yards.
With the Saints flooding the midfield Steven Thomson was enjoying a bit of space on the right wing and his back post cross found Higdon who watched on as his header across goal was hacked away nervously by Bougherra under pressure.
The Buddies, however, were looking confident but on 10 minutes they were almost caught with too many bodies up the park.
After an attacking move had broken down Kevin Thomson sprinted up the park with the ball and played a neat one two with Lafferty before sending it out wide to Bougherra.
The marauding defender again delivered a teasing cross, this time along the deck, but John Potter did brilliantly to get across the six yard box to block Lafferty’s effort.
Bougherra was being a constant pest down the right and on 14 minutes he swung over his third excellent cross but Naismith could only head over although, to be fair, he was at full stretch.
Having dominated the early parts of this encounter the home side started to enjoy their best spell with Andy Dorman seeing a lot more of the ball.
But on 33 minutes Rangers again pushed forward with intent and when Kirk Broadfoot drilled a cross in to the box Steven Davis came out of nowhere to head goalwards.
The ball looked to be sneaking in to the corner of the net but Paul Gallagher dived low to his right to pull off an excellent save. This was the closest that either team came to breaking the deadlock in the opening 45 minutes.
The Saints did have a late flurry with two dangerous corners being taken by Dorman but the Gers’ backline held firm.
And when Davis crossed at the other end Whittaker rose above his marker but his header was easily dealt with by Gallagher.
With four strikers on the bench Walter Smith could have decided on a switch at the interval but he stuck by the same players for the restart.
Miller, Boyd and Novo were told to warm-up immediately and they received a standing ovation from the fans camped in the away stand behind them.
The second-half did start well for Rangers with Lafferty and Naismith linking up and the midfield four playing further up the pitch.
But after a good spell St. Mirren fought back and they should have been in front before the hour mark.
On 57 minutes Bougherra had to clear Higdon’s close range header and the striker was again foiled by the Algerian after his lob over Allan McGregor looked netbound.
Moments later Smith decided on a double switch with Boyd and Miller replacing Naismith and Lafferty but this did little to change the momentum that the Saints were building.
They were now the better team and when David Barron crossed from the left McGregor again had to be sharp to hold Mehmet’s glancing header.
After a disappointing first-half this was now a typical Scottish Cup clash with tackles flying in and both teams driving forward at every given opportunity.
The Saints could sense that this was perhaps their big opportunity to take an Old Firm scalp but they could not capitalise and Rangers will hope that home advantage can help them through to the quarter-final stage when the side’s next meet.