It says much about Aston Villa’s recent decline that a goalless draw with Tottenham Hotspur would constitute an FA Cup shock. Not the greatest, but one nonetheless, and as this game drifted towards its conclusion it appeared as if they were going to achieve just that. The team chasing promotion from the Championship had defended with discipline against the one chasing the Premier League title and looked to have shut them out altogether only for two late goals to shatter their resistance and send a wave of relief through this stadium.

Ben Davies’s and Son Heung-min’s goals were neatly taken and on the balance of play Tottenham deserved to proceed to the fourth round at the expense of opponents who for so long had been top-flight rivals. Spurs dominated possession (71%) and had twice as many shots on goal as Villa – 20 compared to 10 – yet having made nine changes to the team that beat Chelsea here four days ago, Mauricio Pochettino had to watch on as his men toiled. He looked as relieved as most in attendance when Son sealed victory, Tottenham’s sixth in succession, with 10 minutes remaining.

For Steve Bruce the overriding emotion was disappointment. The Villa manager said as much as he reflected on this contest and, in particular, the “big chance” that fell Villa’s way on 65 minutes as first James Chester and then Gabriel Agbonlahor had shots on goal blocked by Tottenham after Alan Hutton had diverted Jack Grealish’s free-kick into the area. Six minutes later Tottenham took the lead and never looked back.

“Overall I’m pleased with the way we have performed,” Bruce said. “The players have done as best they could and that’s all you can ask. What I’ve been reminded of is where we need to get to. Tottenham are a really good side and on a bit of roll.”

Of that there is no doubt yet during the first half in particular the eight-time FA Cup winners looked a shadow of the team that has swept aside all-comers since losing 1-0 to Manchester United on 11 December. Their approach play was slow and disjointed and the overriding feeling was that the sweeping alterations Pochettino had made – understandably so on the back of a traditionally gruelling run of fixtures – were having an effect.

Only Toby Alderweireld and Eric Dier remained from the team that overcame Chelsea and while the starting XI remained strong, containing as it did eight internationals, they could not build attacking momentum.

One of the players rested was Harry Kane, whose absence was explained when the forward tweeted after the final whistle to say his partner, Kate, had given birth to a girl at 7.30am on Sunday. “Amazing feeling,” he wrote, with Pochettino later confirming that was the reason why the England international was left out of the squad altogether. “Congratulations to Kate and Harry,” the Argentinian said. “I think Harry was more tired than his wife. He spent all night in the hospital so we send him [to get] some sleep.”

Kane would have been on the bench had circumstance allowed it and ultimately it may have been he and not Dele Alli who came on for Vincent Janssen following another difficult match for the Dutchman. Positioned as the hosts’ lone forward he failed to make a telling impact and saw his attempt at scoring a first goal in open play for Tottenham following his arrival from AZ Alkmar in July come to an end on 60 minutes.

It proved something of a turning point as Alli’s arrival, along with that of Georges-Kévin Nkoudou 10 minutes later, injected energy and conviction into Tottenham’s display. And it was the pair who combined for the opening goal, exchanging passes before the latter sent a left-sided cross into the area that Davies directed past Sam Johnstone, on his Villa debut, with a glancing header.

It was the Welshman’s first goal for Tottenham since his arrival from Swansea in 2014 and given the cross was behind him, the full-back deserves credit for his reaction and technique.

Son, who was arguably Tottenham’s best player, struck nine minutes later with a sweeping finish following good link-up play between Moussa Sissoko and Kieran Trippier down Tottenham’s right.

“The FA Cup doesn’t understand about level, if you come from League One or the Championship, so I am pleased we showed a solid performance,” Pochettino said. “We can take positives from this game.”

As can Bruce. His team showed great togetherness, defending deep and in numbers prior to a burst of attacking intent in the second half that led to Chester and Agbonlahor’s chances, the latter snuffed out by a perfectly-timed sliding challenge from Alderweireld. With Villa’s focus firmly on returning to the Premier League at the first time of asking – they are 12th in the Championship, seven points adrift of the play-offs – it may also be a blessing for them to have been knocked out at the first time of asking.

“The club’s had a difficult time and we have to get it up and running again,” Bruce said prior to confirming he has made “an inquiry” about Nottingham Forest’s captain, Henri Lansbury. “I’ll do everything I can to make sure Aston Villa is thought of in the same way as Spurs. Given a bit of time, I know I will.”