The leaders handed Hamburg the heaviest defeat in their 52-year Bundesliga history to stay eight points clear of second-placed Wolfsburg at the top of the table and respond in style to recent criticism of their performances by coach Pep Guardiola.
Thomas Mueller, Arjen Robben and Mario Goetze each scored twice for Bayern to sink sorry Hamburg who were beaten 9-2 in the same fixture two seasons ago when they offered their supporters a barbecue by way of apology.
Striker Dost became the first Dutchman to score four times in a Bundesliga game as Wolfsburg led 3-0 and 4-2 before Leverkusen, for whom Son Heung-min bagged a hat-trick, pegged them back to 4-4.
The drama continued elsewhere as Granit Xhaka's last-gasp goal gave Borussia Moenchengladbach a 1-0 win over local rivals Cologne and Sebastian Rudy scored in stoppage time as Hoffenheim triumphed 2-1 against VfB Stuttgart who are now bottom.
Werder Bremen continued their revival with a 3-2 victory over Augsburg and Eintracht Frankfurt beat Schalke 04 1-0 with a second-half goal by Lucas Piazon.
The thriller in Leverkusen was as much down to dreadful defending as anything else.
Dost was left unmarked to head the opener, Naldo made it 2-0 when his low free kick was misjudged by Bernd Leno and Dost again escaped the attentions of the home defence to score with a deft flick, all in less then 30 minutes.
Wolfsburg then helped Leverkusen back into the game with some blunders of their own.
KEEPER MISTAKE
Son capitalised on a mistake by goalkeeper Diego Benaglio in the 57th minute and the South Korean scored again five minutes later after the former Swiss international came rushing off his line.
Almost immediately Son lost possession and Ricardo Rodriguez crossed for Dost to make it 4-2.
Son, the first player in 11 years to be on the losing side after scoring a Bundesliga hat-trick, pulled another goal back before Karim Bellarabi broke clear to equalise with 18 minutes to go.
Leverkusen had Emir Spahic sent off and then Dost had the final word when he got in front of Leno to flick the winner from Vieirinha's low cross in the third minute of stoppage time.
"Every time I scored I thought we had won it but they just kept coming back," Dost told reporters.
Mueller opened the floodgates for Bayern by converting a 21st-minute penalty, Goetze snapped up a rebound two minutes later and Robben curled in the third in the 36th.
There was no let-up as Robben began the second half with another goal, Mueller bent in the fifth and Robert Lewandowski tapped in Mueller's cross. Substitute Franck Ribery and Goetze completed the rout.
"When you play like that...it's enjoyable," said Bayern midfielder Bastian Schweinsteiger. "We worked well, kept it simple and moved well and that makes it easier."
Bayern have 52 points from 21 games followed by Wolfsburg on 44. Gladbach moved up to third with 36, overtaking Schalke and Augsburg who each have 34.
(Writing by Brian Homewood, editing by Tony Jimenez)
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