The 26-year-old Spaniard struck the winner with less than three minutes remaining in an impressive show of character by Chelsea.
The 26-year-old Spaniard struck the winner with less than three minutes remaining in an impressive show of character by Chelsea, after they had been pinned back when substitute Michy Batshuayi headed into his own net eight minutes from time.
"This was the perfect response of champions," Conte told Sky Sports.
"I am very pleased with the will to fight for every ball and they showed me the desire of last season is still there."
While the three points get Conte's side off the mark -- the perfect riposte to their shock opening 3-2 defeat at home to Burnley -- newboys Huddersfield Town made it two wins from two to sit just below leaders Manchester United on six points.
The Terriers, only the third promoted side to ever win their opening two games, beat Newcastle 1-0 with impressive Australian Aaron Mooy scoring the only goal, a delightful curling effort in the second half.
At Wembley, Alonso opened the scoring with a brilliant free-kick in the 24th minute, and while Tottenham pressed hard for the equaliser, Conte's side were unfortunate not to get a second when Willian struck the post in the second half.
It looked as if Conte would have to read more negative headlines on Monday as Batshuayi, who had only been on the pitch for a few minutes, headed Christian Eriksen's free-kick past Thibaut Courtois.
Alonso, though, once again rescued his team by latching onto Pedro's pass and firing past Hugo Lloris, although the Spurs keeper should have saved.
"Unbelievable and at the end in front of our own fans. It couldn't be better," said Alonso, who hopes to emulate his grandfather and father in playing for Spain.
"As for the free-kick, I don't score those even in training let alone a match normally!" added Alonso, who was the last Chelsea player to score an away double having done so at Leicester in January.
The three points and the fact they ended the match with all 11 men on the pitch -- which had not been the case in the Community Shield or their opening defeat by Burnley -- will be encouraging for Conte.
"I want to thank my players because their commitment, their desire and heart they put on the pitch was incredible in what has been a very difficult moment for us," Conte told Sky Sports.
Tottenham counterpart Mauricio Pochettino bemoaned his side's lack of a killer instinct in front of goal -- England striker Harry Kane's August jinx continuing as he has failed to score in his past 12 games played in th month.
"I'm disappointed because we deserved more but they were very clinical with two shots on target and two goals," the 45-year-old Argentine told the BBC.
"We dominated and we were better but if you are not clinical, you can lose like today."
Mooy, an astute purchase from Manchester City after he impressed on loan last season, praised Huddersfield manager David Wagner for their amazing start.
"I don't have to pinch myself but I didn't expect it," said German Wagner, who was plucked from the Borussia Dortmund reserve team job in 2015.
"But it's football, if someone knows that in football everything is possible then it's me and our club after what we've seen and felt last season."