The 28-year-old reached 10 goals for the season as he equalised Kyle Walker's opener for Spurs before levelling for a second time from the penalty spot after Danny Welbeck had been tripped by Hugo Lloris.
The brace also moved Rooney clear of Robbie Fowler and into fifth place in the all-time Barclays Premier League top goalscorer list.
Rooney now sits on 164 goals and Moyes was delighted with his strikers' continued contribution at White Hart Lane.
"He has had a nice weekend," said Moyes. "He is playing well and scoring goals.
"When the moment has come he has taken them. He was very good again today. A goalscorer has always had to score goals. You will see him score a lot of great goals.
"But that was more of a sniff at goal, a mix-up in the box and he was on the end of it. His performances have been great and he worked incredibly hard and he deserves the rewards he has been getting."
Despite Rooney reaching double figures for the season - his total is 12 when England goals are taken into account - the draw in north London means United are now nine points behind league leaders Arsenal.
Former Everton boss Moyes admits the gap is something which he is starting to worry about but wants his side to move closer to the front-runners over the busy festive period.
"We are concerned that we are not as close as we would like to be," he added.
"But it is a long season. We still have got room to progress and get better. That is undoubted. Hopefully we will be there or thereabouts.
"There are a lot of games in the next eight weeks. We hope to be in the mix at the end of that period.
"The Premier League is tight. A lot of games to be played. We will try and stay on the shirt-tails and put ourselves in a good position hopefully coming the end of this year, certainly the start of next year."
United have two home games in the space of four days over the course of the remainder of the week as they look to win their first league game since the victory over Arsenal on November 10.
Moyes will welcome former employers Everton to Old Trafford on Wednesday night before Newcastle travel to Manchester for Saturday's early kick-off.
United's stuttering start to the campaign means both Everton and Newcastle currently sit above the Red Devils in the table and, with Robin van Persie missing with a groin complaint, Moyes will be hoping Rooney's goalscoring form continues.