The Mercedes' drivers fastest times were set on the medium tyre while McLaren used the soft for theirs.
Norris was testing a new front suspension design that is aimed at improving the 'numb' feeling on the front axle that has affected his ability to trust the car on the absolute limit in qualifying this season.
The upgrade was available to both drivers but only Norris used it on Friday. Piastri has been more comfortable with the feel of the front of the car, partly explaining the turnaround in form between them since last year.
Aston Martin's Lance Stroll crashed early in the session, hitting the barrier a glancing blow on the exit of Turn Six and breaking his left front suspension.
His car suffered understeer on the exit of the corner and the front washed out into the wall. Stroll had experienced the situation earlier in the lap but it was exacerbated in the incident by 'dirty air' from the traffic ahead.
A number of other drivers misjudged their braking points and skipped over the grass at one of the chicanes with no damage.
And Alpine's Franco Colapinto had his second spin of the day at Turn Two, after an earlier one in the first session. The Argentine ended the second session slowest of the drivers who set a time.