Spurs were last season mixing it among Europe's elite, beating Inter Milan and AC Milan in the Champions League before being knocked out at the quarter-final stage by Real Madrid - and their class told throughout tonight's contest.
It took little more than four minutes for the visitors to take the lead as Rafael van der Vaart opened the scoring and Jermain Defoe netted a second eight minutes later.
Jake Livermore struck on his third Spurs appearance after 28 minutes as the visitors - playing their first competitive match of the season following the trouble in London - scythed through the hosts' defence once more.
After demonstrating their superior speed and strength in the first half, Gareth Bale did so once more as he netted a fourth after 63 minutes and Aaron Lennon added a fifth after 78 minutes.
A contest billed in some quarters as a 'Battle of Britain' between Scotland's third best side and England's fifth now appears to have ended before next week's return leg at White Hart Lane.
The visitors had to stay 50 miles away in St Andrews as a result of the Edinburgh Festival, while a midfield injury crisis meant 21-year-old Livermore was called upon to start.
A cacophony of noise in Tynecastle met Harry Redknapp's men, whose Barclays Premier League opener with Everton was postponed due to the London riots.
Hearts fans taunted their rivals saying "your city's on fire" - unfortunately for the men in maroon, so were the opposition as Spurs quickly put their troubled build-up behind them.
After five minutes, Spurs struck when Van der Vaart's persistence paid off.
The Holland international was playing off Defoe and hit a one-two with the England striker which Hearts failed to intercept, Marius Zaliukas blasting the ball into the Dutchman.
As a throng of Hearts defenders paused on the edge of the area claiming handball, Van der Vaart played to the whistle and prodded the ball in beyond Marian Kello.
The noise level dropped as Spurs dominated possession, looking like the home side.
After a wayward drive from Hearts' former Tottenham trainee John Sutton, the visitors went 2-0 ahead.
Lennon's pass from the left channel found the onrushing Defoe inside the right edge of the box for a simple finish.
Van der Vaart was a constant threat and he teed up Bale to shoot narrowly off target before Spurs netted a third after a moment's respite which allowed Hearts to experience a small period of possession.
Livermore took the initiative, bursting into the area and combining with Defoe before drilling in.
Defoe had an effort blocked by Jamie Hamill moments later and struck the bar following an acrobatic effort from Lennon's cross, but the striker had been ruled offside.
It was one-way traffic and Younes Kaboul fired over before an optimistic left-footed effort from Ryan Stevenson failed to trouble Heurelho Gomes in the Tottenham goal.
Hearts and Tottenham legend Dave Mackay at half-time said he wished he was playing - the 76-year-old would likely have been talking about playing in white.
Two corners early in the second half had Spurs scrambling to clear, but the hosts were unable to get the decisive touch and then Stevenson deflected Andrew Driver's cross wide.
Hamill had Gomes back-pedalling to palm away a free-kick, but the whistle had already gone for a foul.
Van der Vaart was withdrawn for Tom Huddlestone, who should have done better than shoot wide soon after.
Huddlestone showed his ability moments later, finding Bale, who made it 4-0 after pulling the ball down, rounding Kello and tucking in.
It was Bale's last action as he was replaced by debutant Andros Townsend, and although the Welshman was granted a rest, Spurs were not yet finished.
From a Hearts corner, Spurs burst forward, scything through the hosts' defence. Townsend found Defoe down the left and the striker crossed for Lennon to tap in.
Stevenson shot wide with a minute remaining as Spurs kept a clean sheet and warmed up for Monday's trip to Manchester United in fine style.
New Hearts boss Paulo Sergio, meanwhile, was left to turn his attentions to the Clydesdale Bank Premier League and Kilmarnock on Sunday.