Harry Redknapp's side were enraged when referee Martin Atkinson awarded a controversial strike just after halftime but Roberto Di Matteo's men warmed up for Barcelona in style
Rafael van der Vaart had efforts off the line and against the post in the first half – but Didier Drogba’s sensational turn-and-shot ensured, out of nothing, a half-time Blues lead.
Referee Martin Atkinson incited shock after the restart when he judged that Mata's effort had bypassed a crowd on the line and gone in, though Spurs' anger lifted a little when Bale slotted home shortly after.
A late treble for the Blues, though - Ramires' finish after beating the offside trap and a fantastic free kick strike from Frank Lampard before Florent Malouda's last-gasp fifth - ensured their advancement to face Liverpool next month.
Harry Redknapp surprised some by keeping faith in former Blue Carlo Cudicini as his preferred FA Cup goalkeeper, while Van der Vaart, Emmanuel Adebayor, Scott Parker and William Gallas all also came in after Spurs' loss to Norwich City.
Chelsea, meanwhile, opted for Drogba up front with Fernando Torres a substitute. David Luiz and Ashley Cole returned to the defence, replacing Gary Cahill and Ryan Bertrand.
The game started on a sour note as a pocket of Chelsea fans jeered during a pre-match minute’s silence in memory of those who died at the Hillsborough disaster as well as Livorno midfielder Piermario Morosini.
Once underway, the game started slowly. Drogba had an early chance when he peeled away from his marker chasing a long ball, but mistimed his attempted volley in the box.
Both teams looked cagey but Chelsea needed some great defending when Lampard’s decisive slide tackle robbed Parker in the box.
There was a nervy moment for Spurs in the 26th minute when Chelsea broke forward, Salomon Kalou seizing the ball from Kyle Walker and splitting the defence but Juan Mata, alone in the box, was outpaced slightly by the pass and Cudicini collected safely from his fleeting touch.
Kalou was again involved shortly after when he delivered a nagging cross from the left. Drogba rose to meet it but Ledley King intervened to divert it out.
Spurs nearly took the lead on 36 minutes, however. Lennon received the ball in the box near the right-hand post but spied Van der Vaart advancing from the penalty spot and dinked a short-range cross, but the Dutchman’s header, past Petr Cech, met Terry on the line, whose knee kept it out.
If Adebayor had got a similar touch with his knee when he lunged to meet a stunning right-side cross from Van der Vaart, it might again have been 1-0, but as it was the delivery bypassed both he and Cech before coming back off the post.
And Spurs’ failure to capitalise was punished when Drogba struck. Out of nothing, the striker received the ball with his back to goal. He seemed to be heading away from danger when he touched it to the left, but instead swivelled around Gallas and hammered it left-footed past the helpless Cudicini.
After the break, Chelsea pushed for a second. Drogba battled in the box but reluctantly allowed Mata to strike when his touch fell better for the Spaniard – Cudicini, though, saved well low to his left.
Controversy struck a moment later, though, as an almighty scramble in the box saw players pile up along the line and Mata get a shot into the melee. From some distance away, referee Atkinson ruled that it crossed the line, but television replays appeared inconclusive whilst Spurs protested.
Tottenham, though, got back into it within five minutes. Adebayor powered through the centre and Cech rushed forward to meet him. The keeper brought the Togolese down clearly but was spared a red card as Bale was on hand to knock it into the net on the advantage. Luiz, seemingly badly hurt tussling with Adebayor in the buildup, was instantly replaced by Cahill.
After that explosion of events a brief lull came. King was on hand at the Chelsea some time after, rising for a Van der Vaart corner, but his header was diverted just wide.
Spurs rued that block when Ramires made it 3-1 in the 77th minute. Walker’s deep position allowed Mata to dink the ball forward for the advanced Ramires without fear of offside, the pass picking him out perfectly, and the Brazilian promptly buried it.
The tie seemed confirmed in swift fashion thereafter. A desperate, farfetched penalty shout for a Cahill handball was followed by a free kick for Chelsea at the other end. Lampard stepped up to fire it into the corner from range, a fine hit in keeping with his all-time best.
Tempers flared in stoppage time, with Parker needing restraining by teammates in reaction to a John Obi Mikel kick, but substitute Malouda confirmed the rout by finishing between Cudicini's legs on the end of a Mata assist.
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