The four-time championship-winning outfit had a disastrous pre-season, struggling for pace and reliability throughout the 12 days of running at Jerez and Sakhir.
However, Vettel and Daniel Ricciardo were within one second of the pace in both free practice sessions at Albert Park on Friday, and the two cars logged 115 laps in total.
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"It was very good," said Vettel of Red Bull's day. "It is a big relief, a lot of work went into this.
"Neither of us had big problems today, the cars were running and the balance felt very good.
"At the end of Friday times are not worth a lot but it is better to be closer to the top rather than somewhere lost in the back.
"In terms of speed we know there is a lot more to come but so far it feels very good."
BETTER THAN EXPECTED
While Vettel stressed that reaching the finish on Sunday remains "the most important thing", Ricciardo admitted that the team had exceeded its own expectations with the RB10.
"We were probably expecting to be a bit further off," said the Australian.
"Hopefully the gap doesn't get any bigger but if it stays where it is, within a second is better than expected coming here.
"I won't get too excited but today was a really good day for us. We learned a lot.
"I knew the guys were doing everything they could since testing, but today to get as many laps as we did, we didn't expect that.
"We are really, really happy. This will motivate the team a lot and show that we can overcome any difficulties that are ahead of us still."
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