Mainz make it five wins from five
Coach Thomas Tuchel's team have 15 points from five successive wins, clear of Hoffenheim, who lost 2-1 at home to Bayern Munich, and Hanover 96, 4-1 winners over visiting Werder Bremen.
"With such a performance we could be playing in the (English) Premier League," said Tuchel, the Bundesliga's youngest coach at 37 and whose tactical acumen has won widespread praise this season.
"The fans were great tonight and they were rewarded with two goals. It is just fantastic," he told reporters.
Mainz, promoted to the top flight last year, are now two wins away from equalling the best Bundesliga start ever.
The 20-year-old Holtby, whose father is English and who has attracted the interest of Premier League clubs, repaid his coach's trust, heading in at the far post to break the deadlock against defence-minded Cologne in the 72nd minute.
He sealed the win with a perfect finish past Cologne goalkeeper Faryd Mondragon in added time.
Champions Bayern snatched a stoppage-time winner through defender Daniel van Buyten to move up to seventh on eight points after Bosnian striker Vedad Ibisevic had given the hosts a dream start in less than 60 seconds.
Hoffenheim could have grabbed a second just before half-time but Sejad Salihovic's free-kick from 32 metres rattled the post.
Bayern upped the tempo in the second half with Croatian striker Ivica Olic replacing Toni Kroos.
Thomas Muller's 62nd-minute leveller and Van Buyten's late winner, when he flicked the ball into the net with his knee, gave Bayern their first league goals and win since August 20.
"We did have a bit of luck today but we sort of forced it," said Bayern coach Louis van Gaal. "We put them under so much pressure that we deserved this victory."
However, their success was overshadowed by an ankle injury to playmaker Franck Ribery.
The Frenchman, who set up the equaliser with a solo run and shot that saw Muller score from the rebound, had to be taken off with club officials suspecting a ligament-related injury.
"He could be out for a longer time (than initially thought)," Bayern director Karl-Heinz Rummenigge told reporters.
Werder Bremen, competing in the Champions League this season, continued their dismal start when they slumped to defeat at Hanover 96 to remain in 12th place on four points.
Last season's runners-up Schalke 04 will be desperate to pick up their first points of the season after four consecutive defeats when they travel to Freibu