Nancy suffered a fifth defeat in seven games since taking charge of the Scottish champions as Celtic missed the chance to usurp Hearts at the top of the table.
Motherwell were worthy winners at Fir Park and could have inflicted a far more embarrassing scoreline on Nancy's men but for wasteful finishing in their first home win over Celtic since 2013.
Ibrahim Said stooped to head in his first goal for the club before Elliott Watt capitalised on a mistake from Kasper Schmeichel.
Second-place Celtic's edge over Rangers is down to three points and could be wiped out by Saturday's Old Firm showdown at Celtic Park.
"The message is getting across, but we faced adversity today, and that is the reality. After that comes a bit of doubt," said Nancy, on whether his tactical changes can work.
Rangers secured an eighth win in 11 league games under Danny Rohl but were thankful to a fourth penalty save of the season by Jack Butland.
Thelo Aasgaard headed in the opener before centre-back Emmanuel Fernandez doubled Rangers' lead in the 52nd minute.
Butland saved Marcus Fraser's spot-kick, but League Cup winners St. Mirren still ensured a nervy finale for the home crowd at Ibrox when Mikael Mandron pulled a goal back.
"It's not about two, three, four games - it's about 10 and 11," said Rohl. "We have to perform again and again consistently. At the moment, we are doing this."