The North London outfit battled hard at St Jakob-Park, and had to play extra time with 10 men after Jan Vertonghen received his marching orders late in normal time.
All of the Swiss side's four penalty takers scored in the shootout to send them into the last four of a European competition for the first time in their history.
Here, Sports Mole takes a closer look to see if Spurs have a right to feel hard done by.
On Target: 8
On Target: 12
Was the result fair?
Yes. Over the two legs, Basel were the better team and deservedly progress to the semi-finals.
The hosts didn't get out of the blocks very well. Spurs had the better opportunities of the first half, but Murat Yakin's men managed to get into half time level. They went ahead in the second half and looked very comfortable until Clint Dempsey's goal evened things up. They began to look tired and nervous as Spurs came on strong, but Jan Vertonghen's red card gave the initiative back to them. The Swiss side put pressure on the Spurs defence in the second period of extra time, but couldn't find the killer goal. However, some cool penalty taking ensured their passage into the last four.
The North Londoners were the better side in the early exchanges. They had the better of the first half, but still trailed on away goals at the break. For large parts of the second half, they struggled to break down their opposition. They managed to get back into the game and then looked like they might be able to win it, only to be reduced to 10 men and forced to batten down the hatches. Heroic defending from Michael Dawson helped secure a penalty shoot-out, but Tom Huddlestone and Emmanuel Adebayor were the fall guys as they missed from the spot.
Sports Mole's man of the match
Michael Dawson: The centre-back was out on his feet at the end but he was integral in ensuring that Spurs got the tie to a penalty shootout.
Aleksandar Dragovic's hashed clearances gifted Dempsey the chance to grab the first goal of the evening, which he duly took. It was a complete shambles, and that's being kind.
Olegario Benquerenca was kept busy tonight, mainly due to the wet surface making it tricky. He handled the occasion reasonably well, and there were no big errors. His decision to send off Vertonghen was correct.
Basel: The Swiss side have never made it to the semi-finals of a European competition before and they will find out who they play in the last four tomorrow. However, they host Zurich to St Jakob-Park in domestic action on Sunday.
Spurs: Andre Villas-Boas's men have nine days off now before they welcome Manchester City to White Hart Lane on April 21.