Jermain Defoe grabbed his 16th goal of the season with an expert poacher's finish as Rangers earned a nervous but valuable win against St Mirren in front of almost 50,000 at Ibrox.
Defoe could have added another midway through the second half but failed to latch onto Nikola Katic's header.
St Mirren applied some late pressure, but couldn't make their set-pieces count, as Rangers remained two points behind leaders Celtic, who won 3-1 at Kilmarnock.
How Rangers did just enough to keep the pressure on
Steven Gerrard had criticised his fringe players' impact and confessed to being "bored" with the performance during Rangers' 2-0 Scottish Cup win over Stranraer last Friday, and he will not have been impressed by his team's wastefulness here.
Gerrard restored the bulk of the side that beat Celtic in the final game before the league's winter break in December - Allan McGregor, Connor Goldson, Borna Barisic and Glen Kamara all started at Ibrox.
This was the first of five league games for Rangers in 14 days, four of them at home. Barisic's freekick had been the difference when the sides met in Paisley in August, and the Croatian fullback nearly created an early chance for Joe Aribo, as his whipped cross was deflected into the arms of St Mirren 'keeper Vaclav Hladky.
The visitors were dealt a huge below inside the first five minutes as captain Kyle Magennis was stretchered off and replaced by Ilkay Durmus. The Turk almost made an immediate impact on the left, as his hopeful cross looped onto the crossbar and away from danger.
Defoe started up front for Rangers once more with Alfredo Morelos suspended, but St Mirren's defensive discipline meant he had few sights of goal in the early stages. Instead it was Nikola Katic, with a header over the bar, and Ryan Kent, whose shot was blocked on the angle by Hladky, who came closest in the opening half hour.
Barisic was causing havoc on the left, twisting makeshift fullback Ryan Flynn inside out on more than one occasion, but despite incessant pressure a final decisive pass was lacking. When the opening goal did come after 33 minutes, it was more by luck than design.
A cross from the right was cleared out to Barisic on the left corner of the box, and he took a touch before scuffing a low shot into the box. The ball deflected off Flynn and into the path of Defoe, who expertly flicked it into the far corner.
In first-half stoppage time Rangers' lead should have been extended, as a corner found Katic six yards out and he stabbed it towards goal, only for Paul McGinn to clear off the goal-line and into Hladky's grasp.
The second half began much the same way as the first concluded, with Rangers dominating possession but huffing and puffing once they reached the St Mirren penalty area.
There wasn't another clear-cut opportunity until the 66th minute, when Katic headed Davis' freekick across goal, but Defoe was unable to finish at the back post. Scott Arfield came on for Glen Kamara and immediately blazed a long-range shot over the bar.
With the lead precarious the tension inside Ibrox was audible, as supporters vented their frustrations at the lack of creative spark. A Barisic freekick caused chaos in the St Mirren defence, but somehow evaded a cluster of bodies at the back post as Rangers tried to end the game as a contest.
The visitors had a rare chance from a corner, but it ended in calamity as Akin Famewo and Jon Obika both connected with the ball - and with each other's heads, resulting in some lengthy treatment.
In the final minutes, substitute Sheyi Ojo saw a shot deflected wide, before Hladky saved Arfield's half volley.
St Mirren then won a corner in stoppage time, but it came to naught, and Defoe missed another chance on the break after being set up by Kent, but Rangers had done enough to secure the points.
What the managers said...
Rangers boss Steven Gerrard admitted he was more pleased with the defensive play than the attacking performance.
He said: "I thought defensively we were excellent. I understand supporters and even some of my players expect us to win more comfortably, and are probably a little bit frustrated we never got the second goal and the third goal - I get that.
"But, I am delighted. It's another win, it's a clean sheet and it moves us closer to where we want to be. Over the course of a season, if we manage to go on and make it successful, every game isn't going to be perfect: it's about winning and finding a way.
"Of course we could maybe have created a little bit more or killed the game off at the end when we have had some real, decent half-chances, but it wasn't to be. The main thing is we have got over the line."
Ahead of their Tynecastle test, Gerrard admitted it would be a difficult game.
He added: "You have a manager trying to implement more of a footballing team. Hearts are trying to play out and they are also trying to press and be aggressive.
"We do expect a different type of challenge - same personnel, same environment, but we are expecting something different as it is a different manager with his own ways. It will be a tough challenge but one we will be ready for."
St Mirren manager Jim Goodwin bemoaned the serious-looking injury suffered early on by Buddies captain Magennis.
He said: "It's not looking great. He's our captain on the night and he does a fantastic job for us.
"He's going for a scan on Thursday morning but at this moment in time it's not looking good.
"He's definitely done ligaments, it's just a question of whether it's medial or cruciate. If it's the medial it's six to eight weeks, if it's the cruciate it could be season-ending.
"To lose a player as influential as Kyle, with such a serious injury, is so disappointing for him - and he's going to be difficult to replace."