Keane, who finished last season on loan at Celtic, played the first 45 minutes but could not get on the scoresheet.
Strike partner Jonathan Obika took advantage of a defensive error to open the scoring after 36 minutes before two second-half goals in a little over a minute made life more comfortable for the Barclays Premier League side.
Roman Pavlyuchenko scored in the 61st minute after good work from Andros Townsend, then the same pair combined a minute later to set up Danny Rose for the third.
Spurs hit the woodwork twice through Adel Taarabt and Townsend, before Pavlyuchenko grabbed his second 16 minutes from time after latching onto a long ball from Younes Kaboul.
The only disappointment for Spurs was the sight of David Bentley limping off in the first half.
Everton also kicked off their pre-season preparations on Saturday as Victor Anichebe found the net to secure a 1-0 victory over Sydney FC in Australia.
The striker scored a minute into the second half, receiving a pass from Leighton Baines and turning well before shooting into the roof of the net.
Australia international Tim Cahill received a tremendous reception from the 40,000 strong crowd inside the ANZ Stadium when he came on at half-time.
There were no such goalscoring exploits by Blackburn, who played out a goalless draw against Sturm Graz in Austria.
On a hot day at the UPC Arena, there were few chances for either side, but it was the Austrians who had the better of the play, especially in the first half.
Source: PA
Source: PA