Dundee United booked their ticket for Monday's Scottish Cup semi-final draw with a deserved 2-1 victory over Dundee at Dens Park.
The home side, 15 points adrift at the bottom of the SPL, could not recover from the concession of two soft first-half goals, despite Jim McAlister offering a brief glimmer of hope.
United took the lead when Brian McLean (11) was given the freedom of the penalty area to glance home a header from Barry Douglas's inswinging free-kick.
Dundee levelled as John Baird helped the ball into the path of McAlister (19), who drilled a low first-time strike into the corner from 15 yards.
The equaliser heralded the best spell of the match for the Dark Blues as Baird headed over before the home striker saw his low shot saved by the feet of Radoslaw Cierzniak.
United were promptly back in front as Stuart Armstrong teed up the lively Gary Mackay-Steven (35) with a shrewd pass and the midfielder did not have to break stride before drilling in a snap-shot from 18 yards.
Michael Gardyne worked Rab Douglas at his near post while Lewis Toshney's risible free-kick from 30 yards underlined the hosts' growing frustration.
A flurry of Dundee corners yielded nought until Davide Grassi made some space eight yards out but his header was tame.
Jon Daly was inches away from poking home a third goal for United, but it was not to matter, the final stages pockmarked only by a flurry of needless yellow cards.
The Glasgow giants headed into the break at Ibrox trailing to an Andrew Stirling strike and in danger of suffering an upset as they edge closer to the Scottish Third Division title.
McCulloch felt too many players were trying to steal the headlines for themselves and the skipper let his feelings be known in the dressing room.
Rangers then hit back through a McCulloch goal and a double from Andy Little to secure the points in the second half.
The Gers captain said: "In the first half it was a team of individuals but I thought in the second half we played as a team better.
"That showed in the result and the performance. The boys were having a wee go at each other at half-time, which was needed. We knew it wasn't good enough.
"After having a chat with each other, it showed in the second half, when we came out to play some good stuff at times."
He added: "I think the most important thing is team performance. In the first half, I think there were a couple of individuals trying to make the headlines with shots from the byline and stuff like that instead of playing as a team and wanting to win as a team.
"It's not an individual game and I think that annoyed a couple of people. In the second half, we played as team."
The visit of the Shire was McCulloch's first outing since early January after being sidelined with an ankle problem.
He said: "It felt great to be back. I was a bit nervous before the game.
"I was out for about seven weeks and only had two days training so I felt a bit tired with 10 minutes to go but I really enjoyed it."
The victory followed an eventful week for Rangers, which saw them found guilty of breaching Scottish Premier League rules over non-disclosure of payments to players between 2000-2011, with the oldco fined ?250,000.
But they were celebrating after the independent commission ruled no sporting advantage was gained, meaning the Light Blues avoided the ultimate sanction of being stripped of up to five titles.
McCulloch says a win was important to cap an important few days for Rangers - but claimed taking a step closer to wrapping up the championship was the main motivating factor.
He said: "I'm sure it's been a good week for the fans and it's been a good week for the players and the staff and everybody.
"But the most important thing was keeping this title charge going and looking to win the league."
Shire boss John Coughlin had nothing but praise for his players despite the defeat.
He said: "I thought we were excellent.
"We knew there was a storm coming in the second half because the Rangers fans would not be happy being a goal down to the Shire.
"But I thought we enjoyed the game and passed it about well."
