The score predictor had dropped to 229 runs from 310 at the start of the game.
Pat Cummins departed for just 6 runs through Rashid's delivery as Root got handed the easy catch.
Smith stood firm throughout and relished solid support from all-rounder Mitchell Starc. Together, they managed to post 43 runs on the scoreboard.
Smith was run out for 85 in the 48th over and Australia could not last their full quota of 50 overs. They tried to replicate the angle of a couple of Australia bowlers - Mitchell Starc, in particular - would pose. In his 9-over spell, he claimed three wickets with an exceptional economy of 3.78.
There were scattered clouds on a sunny and warm morning in Birmingham.
Morgan's side have established a proud recent record against Australia, winning 10 of the last 11 one-day internationals between the old rivals prior to this tournament.
Australian coach Trevor Bayliss was drafted in, sparking an impressive transformation that has seen England climb to number one in the ODI rankings and move to within touching distance of World Cup glory.
Morgan has no doubt England can overcome the reigning world champions and he feels the country is willing his team to achieve something special.
Jonny Bairstow- This English opening batsman has smashed two consecutive centuries in the most crucial stage of the tournament for the team, which eventually helped them to finish at the third position in the points table.
The match will be shown on the Star Sports TV network and DD Sports.
The hosts will have the chance to lift the trophy for the first time when they meet New Zealand at Lord's on Sunday.
But Morgan urged England to avoid being overawed by the scale of the task confronting them in Birmingham.
England are a team on the back of setbacks finally getting the conditions they work best with, a flat deck, one short boundary and they made the most of it. India were nowhere near bad, but England did their thing, just as they had in the years preceding the World Cup while they built their reputation as the team to beat.
Jason Roy has missed three games through injury but still possesses 341 World Cup runs to his name at an average of 68.2.
The most recent of those painful defeats came in 1992 when Graham Gooch's side were beaten by Pakistan, while Australia in 1987 and the West Indies in 1979 have also denied England in the final.
Liam Plunkett believes this England side are "a different animal" to their predecessors and "can beat anyone in the world" if they play well.