After five games without a victory at Anfield, United were again struggling, even against a side reduced to 10 men following the first-half dismissal of Jonjo Shelvey.
And when Steven Gerrard struck straight after the interval, it seemed the Red Devils' unhappy recent record on Merseyside was going to be extended.
Instead, Rafael curled home a superb equaliser, which allowed United to create the platform from which Robin van Persie eventually secured maximum Barclays Premier League points with a late penalty.
"It was an important time to get the goal," said Rafael.
"It was a good moment to get it because it was so quickly after they scored. If we hadn't scored then we might have got a little bit nervous."
Amazingly, Rafael has now scored twice this season after also finding the target against Fulham last month.
It leaves him second in United's scoring charts, trailing only Van Persie, who heads the Golden Boot standings with five.
Rafael is benefiting from his Olympic experiences with Brazil over the summer, even though he eventually had to settle for a silver medal in London.
At the time he expressed a hope that Premier League crowds would start to appreciate his all-action approach.
That is certainly the case at Old Trafford now, even if some reservations have been held about his impetuous nature.
Sometimes it can easily be forgotten Rafael was only 22 in July and is still making massive strides in his fledgling career.
"It's definitely the best goal I've scored for United," he said of Sunday's excellent effort, a curling left-footed strike that bounced in off a post.
"I have scored four goals for United now, one with my head and two with my left foot. Maybe I am better with the left."
With Phil Jones and Chris Smalling both ruled out with long-term injuries, Rafael has cemented his status as Sir Alex Ferguson's first-choice right-back.
And he is doing it without the presence of twin brother Fabio, who has joined QPR on loan.
Rafael threatened to ring his brother in the immediate aftermath of United's victory, although after Rangers lost at Tottenham, maybe it would have been better to hold off for a little while.
Indeed, a period of quiet contemplation might be better for everyone after such an emotional day, which had gone so well until a mindless pair of Liverpool fans took it upon themselves to goad a still packed away end with aeroplane signals long after the final whistle.
The reaction was sad and predictable.
United opted not to respond to the anti-Liverpool chants that were clearly heard by those still present in the stadium and captured by TV cameras after the match.
Indeed, there is little more the club could have done to plead with their supporters to behave, and have been commended for the way in which they carried out pre-match gestures.
None of this was of major significance in the dressing room afterwards.
After that shocking opening weekend defeat at Everton, United have recorded four straight victories, leaving them just a point behind leaders Chelsea and three in front of title-holders Manchester City.
"Both clubs have a great history and we had to respect that, then we got the three points, which is so good for us," said Rafael.
"It wasn't a great performance from us but in the last five years we haven't won here so we're very pleased.
"Robin van Persie had to wait a long time to take his penalty. It might make some people anxious but he is a top player and he found the net."