The Ibrox outfit's third consecutive league away win was earned at Dunfermline by an Andrei Kanchelskis volley and two goals from Jonatan Johansson.
But Advocaat's night was spoiled with 15 minutes remaining when he disputed a controversial penalty award, venting fury at the referee, Willie Young, for adjudging Kanchelskis to have pushed the Dunfermline substitute Colin Nish.
Andy Smith, the Dunfermline captain, put the penalty wide, but Advocaat's broadside at the official continued and after a heated discussion Young pointed him out of the dug-out.
The Scottish Football Association's disciplinary committee next meet on 15 March. An SFA spokesperson said yesterday: "We expect to receive the referee's report on Tuesday, and then the usual procedure is that a copy will be sent to all relevant parties.
"If Dick Advocaat is to be disciplined he will be asked for his comments and then whether he wants to appear in person in front of the disciplinary committee to state his case."
The only encouraging aspect for Advocaat is that the championship race could be virtually over by the middle of next month with Rangers so dominant.
Rangers, who have played a game more than their rivals, are 12 points ahead of Kilmarnock and 13 clear of the reigning champions, Celtic, with only one further Old Firm meeting remaining between the Glasgow clubs.
Celtic's problem is that teams who took points off them with relative ease earlier this term are showing few signs of doing the same to Rangers in the campaign's latter stages.
Advocaat was still less than satisfied with the overall quality of Rangers' showing at Dunfermline - describing the opposition as the sharper side - but paid tribute to Kanchelskis.
He said: "They refused to give us a chance to play football in the first half, but the quality of Rangers is such that we can score at the right time, and all three were excellent goals."
Lorenzo Amoruso, the Rangers captain, is in confident mood because he senses the team are still improving as a unit and he considers they have yet to reach their peak.
He said: "As the season progresses we are becoming stronger in many aspects of our play, but we are taking nothing for granted at the moment - the manager would not allow us to.
"He made it clear to us how important this trio of away games were, and we have won the lot with the kind of consistency which shows we don't intend to falter at this stage."
Dick Campbell, the Dunfermline manager, gave Rangers a better match than the eventual scoreline suggests and reckons the same approach from his men can steer them to Premier League safety. His mood was cheered by Andy Tod's decision to snub interest from both sides of the border and agree a new four-year contract.
Campbell said: "There has been interest in him, but that is no surprise because he's a quality player, the test of that being how few matches he has missed in his time here.
"If he completes this next four years that will be a decade at the club, and I personally hope he will stay another four after that because he is a big player for us and a magnificent ambassador."Reuse content