Kuipers played the first 15 minutes in goal for the Seagulls before being replaced by Tomasz Kuszczak, but it took a penalty for Brighton to open the scoring.
Alex Pearce conceded the spot-kick after 32 minutes, upending Ashley Barnes, with Vicente Rodriguez stepping up to convert the penalty.
Some bright play from Reading yielded results in the second half though, with Robson-Kanu eventually levelling the scores on the 90-minute mark.
Billy Sharp managed to salvage a 1-1 draw for Southampton as they clashed with Bristol City at at Ashton Gate.
The home side took the lead through Jon Stead after 36 minutes but Saints, who had Olympic player Jack Cork back in the side, levelled the score as Sharp knocked home a far-post shot at the death.
Craig Dawson was another to suffer Olympic disappointment with Team GB, but he featured on the scoresheet as West Brom saw off fellow midlands club Walsall 3-1.
Dawson gave the Baggies the lead when heading home Yassine El Ghanassy's 16th-minute corner while Saido Berahino doubled the margin after 62 minutes.
El Ghanassy secured his first Albion goal in the 87th minute while George Bowerman scored a consolation effort for the home side with a minute to go.
Hugo Rodallega made an immediate impact for Fulham by notching a late winner in their penultimate pre-season friendly at MK Dons.
The ex-Wigan Star joined Fulham on a three-year deal last month and he made the most of an opportunity in the six-yard box after 81 minutes to seal a 1-0 win for the Whites.
Norwich gave plenty of players a run out as they were held to a 0-0 draw by Hull at the KC Stadium.
