Thiago Alcantara struck twice and Arjen Robben, Robert Lewandowski and substitute Thomas Mueller were also on target as the Bayern inflicted Arsenal's first defeat of the season in Europe's premier club competition.
Alexis Sanchez had equalised for the visitors, scoring on the rebound after Manuel Neuer saved his 30th-minute penalty but the Gunners suffered when captain Laurent Koscielny limped off injured to leave the defence exposed.
Robben said Bayern had proved their recovery from a recent dip in form.
Bayern, who knocked out Arsenal at this stage of the competition in 2005, 2013 and 2014, got off to a perfect start when Robben curled an unstoppable trademark left-foot shot into the top corner of David Ospina's goal.
Arsenal levelled after being awarded a penalty for a handball by Lewandowski and Sanchez hooked home on the rebound after Neuer saved his spot-kick.
The game looked to have lost its pace early in the second half before Bayern stepped on the gas to fire three goals past the English side who collapsed when Koscielny went off injured in the 49th minute.
Lahm floated a perfect cross into the box and Lewandowski rose high above defender Shkodran Mustafi to drill in a header in the 53rd minute.
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Bayern Munich's Robert Lewandowski scores their second goal against Arsenal Reuters
The Poland striker set up Thiago with a perfect flick for Bayern's third goal three minutes later and the Spaniard grabbed his second with a low drive before substitute Mueller completed the rout two minutes from time.
The English team are on course for a seventh last-16 exit in a row as Bayern close on a sixth successive quarter-final appearance.
The sides meet in the second leg in London on March 7.
Meanwhile, Casemiro's stunning volley crowned a superb display from Real Madrid, who fought back to beat Napoli 3-1 at the Bernabeu in the first leg of their Champions League last 16 tie on Wednesday.
The Brazilian midfielder thundered a spectacular right-foot shot into the net early in the second half to complete Real's comeback, adding to efforts either side of halftime from Karim Benzema and Toni Kroos.
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Real Madrid's Karim Benzema in action with Napoli's Raul Albiol Reuters
Napoli, the top scorers in Serie A, grabbed an early goal when Lorenzo Insigne spotted keeper Keylor Navas out of position to curl the ball home from distance, but when Real clicked into gear they created chances at will.
Holders Real, who are chasing a 12th European title and eyeing a seventh straight quarter-final appearance, will travel to Naples for the return leg on March 7.
Real were defending an enviable home record in the Champions League, having gone 11 games undefeated at the Bernabeu, but were facing a Napoli side in form, unbeaten in their last 18 matches in all competitions.
The hosts were at the throats of their opponents within moments of the kickoff as Benzema forced a reflex save from Pepe Reina with barely 20 seconds on the clock.
At that point it looked like it could be a long evening for Napoli, but the Italians were in no mood to lie down and took the lead to cap a frenetic opening after eight minutes.
Insigne was fed through by Marek Hamsik and spotted Real keeper Navas out of position. Quick as a flash and with two defenders closing in, he bent a shot into the corner from 35 metres.
The lead lasted 10 minutes as Real drew level when Dani Carvajal's arrowed cross was headed powerfully into the net by Benzema, his 51st Champions League goal, lifting him into fifth on the all-time scorers list.
The remainder of the half was spent mainly in Napoli territory as Real continued to press, with Cristiano Ronaldo blasting over after being set free by Luka Modric and Benzema clipping the outside of the post when through on goal.
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Real Madrid's Cristiano Ronaldo shoots at goal Reuters
Their dominance, however, was rewarded four minutes after the restart as Ronaldo skipped to the byline and pulled it back for Kroos on the edge of the box to sidefoot calmly past Reina.
Four minutes later Casemiro took the game, and perhaps the tie, away from Napoli with a stunning right-foot volley from 25 metres that left Reina flailing.
Real Madrid 3
Benzema 18, Kroos 49, Casemiro 54 Napoli 1
Bayern Munich 5
Robben 11, Lewandowski 53, Thiago 56,63, Mueller 88 Arsenal 1