Ex-Barcelona boss Guardiola took charge of the Champions League winners eight weeks ago after predecessor Jupp Heynckes had steered Bayern to the treble of European, league and cup titles last season.
It was a brighter start in the German league for the Spaniard at Bayern than at Barcelona in La Liga, where the 42-year-old lost his first game 1-0 to CD Numancia in the 2008-09 season before going on to win 14 titles in four years.
"We're pleased to have won the first game," said Guardiola. "We need results in the first three or four games, because some players are not yet one hundred percent fit.
"We could have controlled the game better in the first 15 minutes of the second half, but that'll come."
Having broken or equalled 25 records in winning last season's Bundesliga title by 25 points, defending champions Bayern earned their first three points of the new season at home with Arjen Robben and Mario Mandzukic scoring early on.
Left-back David Alaba then converted a second-half penalty after 'Gladbach
defender Alvaro Dominguez gave away two penalties -- both for handball -- in as many minutes.
"Both penalty decisions were correct by the referee, I would have given them, as well," said Guardiola.
The only blot on Bayern's copybook was a Dante own-goal which left Gladbach
2-1 down at the break.
"It is important to win your first game, so that was a good start," said Bayern captain Philipp Lahm.
"After we conceded the goal, the opposition got a little momentum, but we're happy that after our 45 days of preparation the season has started again."
Robben, who scored the winner in May's Champions League final, latched on to a pass from Franck Ribery, just as he did at Wembley, and lobbed goalkeeper
Marc-Andre ter Stegen on 12 minutes for a 1-0 lead.
The hosts doubled their lead four minutes later when Mandzukic, playing as the lone striker, got on the end of Robben's free-kick and stabbed the ball home from close range.
Bayern could have finished the first half with at least four goals as Ter Stegen palmed a Toni Kroos shot onto the crossbar while only a fine tackle from Austria defender Martin Stranzl denied Robben with the goal at his mercy.
The visitors pulled a goal back when Bayern's Brazil defender Dante went to clear the danger from a 'Gladbach attack, but turned the ball into his own net on 41 minutes.
Kroos hit the woodwork again with an hour gone before 'Gladbach's Spain defender Dominguez gave away two handball penalties in as many minutes during a bizarre passage of play.
With Bayern pressing, Dominguez palmed the ball down to concede the first, but Thomas Müller had his penalty deflected away by Ter Stegen.
The ball went straight from Ter Stegen's glove to Robben on the edge of the area and when Dominguez went into challenge, the ball again deflected off his hand and referee Tobias Welz pointed to the penalty spot before booking the incredulous Dominguez.
Second-time around, left-back Alaba drilled home his spot kick to make sure of the three points to leave Guardiola delighted.
"We ran and attacked a lot, we're happy we won, because it was a difficult game," said France winger Ribery. "We had a lot of fun."