Keane's 39th minute spot kick, after a harsh handball decision against Reading defender Greg Halford, secured a fifth successive league victory for Tottenham who face Sevilla in the UEFA Cup quarter-finals on Thursday.
The home side were made to sweat all the way to the end after missing a stack of chances while Marcus Hahnemann and his halftime substitute Adam Federici made a string of fine saves in goal for Reading.
Steed Malbranque hit the post in a bright start for Tottenham and substitute Jermaine Defoe had a late effort ruled out for offside, while the closest Reading came was a header from Leroy Lita that rebounded off the post.
With fifth and sixth places guaranteeing UEFA Cup football next season, Tottenham have a two-point cushion over seventh-placed Everton who play at struggling Aston Villa on Monday. Reading stay in eighth place.
Manchester United still lead the title race by six points after they beat Blackburn Rovers 4-1 on Saturday. Chelsea stayed in touch with a last-gasp 1-0 win at bottom club Watford.
