With all six members of each team putting in high-calibre performances on all four apparatus, the defending champions grabbed the top spot on the final rotation with a combined score of 152.436.
They led the Americans by just 0.588 points while early trailblazers Russia slipped to third on 149.420.
The Romanian-American duel set up an intriguing showdown for Tuesday's team final.
"Our whole theme was to go aggressive no matter what happens because if you're aggressive, you won't have any regrets," American squad captain Mohini Bhardwaj told Reuters.
"I'm so glad we have team prelims before the team finals, it gives us a chance to work out the nerves."
American Carly Patterson gained a psychological edge for the all-round competition when she edged past Sofronie to lead the standings with a total of 38.337. Russia's Svetlana Khorkina trailed in fifth place.
Patterson's Arabian double front balance beam dismount earned her 9.725 and sent her coaches into raptures as they exchanged high-fives.
BOTCHED VAULT
A botched vault by Khorkina had earlier failed to stop Russia from taking the early lead.
Such is the depth of talent in the Russian women's team, which also includes double Olympic champion Elena Zamolodchikova, that they were able to shrug off Khorkina's personal heartache.
World all-round champion Khorkina landed her first vault to earn a respectable 9.512 from the judges but seconds later she over-rotated on her double twisting combination and fell head-first on to the mat before rolling sideways off the marked area.
A stunned Khorkina examined her grazed knee before looking up to the scoreboard for the judges' verdict. It flashed up with just 8.700, leaving the despondent Russian to regain her composure before the final three rounds.
Under Olympic rules, only Khorkina's higher score counted towards the team total. But for the individual competitions the two scores are averaged out.
The temperamental Khorkina went on easily to outclass the opposition with an exquisite routine on her signature apparatus, the asymmetric bars, to record 9.750.
Zamolodchikova, who has been plagued by injuries since her double success at the Sydney Games four years ago, was also below par and recorded her highest score of 9.462 on the vault.
