The Welshman scored twice and provided one assist to help Spurs re-ignite their push for a top-four finish.
Jose Mourinho's side had lost of their six Premier League matches but went ahead inside two minutes when Bale converted Son Heung-min's low cross.
Lucas Moura then made it 3-0 before half-time after Sergio Reguilon's cross fell into the box.
Son opened his legs to provide the fourth through Bale, who was allowed to cut back on his left before curling a shot off the post and in.
Spurs are now six points behind fourth-placed West Ham with a game in hand.
Speaking after the game, Mourinho said: "I don't think it was a performance from another galaxy but we were solid.
"We needed a game where the players could express themselves against a team that never gives up.
"Until the last minute, we had to defend two corners. We had a clean sheet because we wanted a clean sheet. It's something we've not been having."