The Blues were already ahead, courtesy of Chris Riggott's early own goal, when Elano took Michael Johnson's short pass and buried it in the bottom corner.
Then, as City looked to finish Boro off in the second half, up he stepped again to curl a free-kick into the top corner - which Mark Schwarzer had no chance of keeping out.
It is little wonder the 26-year-old was afforded a standing ovation when he was replaced by countryman Geovanni late on.
"Elano has always been an important player for us," said Eriksson.
"If we give him the ball, we know he will keep it - and now he is starting to score goals as well, so I can't ask for any more than that.
"He is fitter and stronger and works in the gym as well, which is good.
"Maybe he will not maintain that standard all the time - but maybe sometimes he will do even better. I certainly don't need to teach him about football."
Eriksson's one concern is that he will not see his star man again until a week on Friday, because Brazil are due to start their 18-match World Cup qualifying programme in Colombia.
The Swede also confirmed young midfielder Michael Johnson is struggling with a groin injury which may yet require an operation.
Eriksson has cleared Johnson to report for England Under-21s duty on Tuesday - but rather than tackle Montenegro on Friday night, the teenager may be heading for surgery which could rule him out for a "few weeks".
"Michael is not 100%," said Eriksson.
"He trains one day, then he misses one - and this has been going on for quite a long time now.
"He is going to report for duty with the England Under-21s squad on Tuesday, and we will take it from there. He might require an operation, or they might think he can recover totally."