Walcott pounced in the late kick-off at Loftus Road in West London just moments after Gareth Bale, newly crowned English player of the year, had celebrated a spectacular winner as Spurs beat Southampton 1-0 in North London.
Bale cut inside from the right and held off a defender before firing home from 25 metres in the 86th minute against his former club.
Callum McManaman scored in the 80th minute at the Hawthorns to give Wigan a 3-2 win over West Bromwich Albion after Roberto Martinez's team had twice fallen behind.
Villa left Carrow Road with a 2-1 triumph over Norwich City courtesy of Gabriel Agbonlahor's double, including the 89th-minute winner.
"Our effort after playing on Monday night [in a 6-1 victory over Sunderland] was outstanding," Lambert told the BBC.
"Agbonlahor has been playing excellently for us. He has the speed to hurt teams, and power as well.
"We have to keep going but it's another huge, huge win. This team is getting better and better every single game."
"We showed our character and never accepted defeat," Martinez said. "To come back twice from behind at a place as difficult as this is huge.
"We have worked really hard for two months to get us in the position where, with two weeks of the season left, we are still involved in two competitions. If we stay up it would be like winning the title."
