All four Spurs goals came in a storming second half after Morgan Rogers put the visitors ahead in the first period.
Brennan Johnson pulled the rejuvenated home side level shortly after half-time.
Solanki then took centre stage, producing a delicate dinked finish to put Spurs ahead in the 75th minute before converting substitute Richarlison’s cross four minutes later.
James Maddison added gloss by firing home a free kick deep into stoppage time.
The result lifts Ange Postecoglou’s men to seventh in the table on 16 points - two behind Villa, who missed out on the chance to climb into third spot.
Meanwhile, Moises Caicedo’s strike denied Manchester United victory in their first Premier League game since sacking Erik ten Hag as Chelsea claimed a 1-1 draw at Old Trafford.
Interim boss Ruud van Nistelrooy, who will be replaced by Ruben Amorim later his month, sprinted down the touchline in celebration after Bruno Fernandes put United in front from the penalty spot 20 minutes from time.
Caicedo quickly replied for the Blues, who edge above Arsenal on goal difference into fourth place in the table.
A point leaves United still down in 13th, six points off the top four.
The Red Devils’ return of just 12 points from 10 games is United’s worst start to a league campaign since 1986/87.
Amorim was not in attendance as he prepares to take charge of Sporting Lisbon for the one of the final times against Manchester City in the Champions League on Tuesday.
United were far more competitive than in 3-0 demolitions by Liverpool and Tottenham at home this season, but showed many of the same flaws that cost Ten Hag his job.
Van Nistelrooy enjoyed a 5-2 demolition of an under-strength Leicester in his first match in charge to reach the League Cup quarter-finals in midweek.
Still a hero among the United fans from his days as a prolific striker, the Dutchman’s name was chanted in a buoyant pre-match atmosphere.
However, a Chelsea side that have lost once in nine Premier League games, provided a much stiffer test for a United side still short on confidence.