Tuesday's floodlit success ensured England kept their series with the world champions alive at 2-1 down with two to play ahead of Friday's encounter across the Pennines at Headingley, the Leeds headquarters of Yorkshire.
Jason Roy (63) and Morgan (62) - who shared a third- wicket partnership of 119 with Taylor (101) -- also made telling contributions.
England were able to frustrate Australia with 20 overs' worth of spin that yielded five wickets for 73 runs.
Morgan, asked about Ali and Rashid, told Sky Sports: "I thought they were outstanding. I think it was set up by the start, we knew the first 15 or 20 overs with the new ball was going to set the tone for us with the ball because it was a lot easier on this particular wicket facing the new ball.
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"I think Steve Finn's spell up the top was really impressive, and then for the two spinners to come on and bowl with control -- they didn't really bowl that many bad balls throughout their 10 overs.
Man-of-the-match Taylor's century was his first at this level and Morgan said: "I think the games we've played so far the top score before that was 85 so we want guys to make match-winning contributions and James Taylor managed to do that today.