"I'm not going to get too down", she said after her 2-6, 7-6 (7/2), 6-2 defeat.
Bencic warmed up for the Australian Open by combining with Roger Federer to win the Hopman Cup for Switzerland.
The seventh seed raced through the first set on Rod Laver Arena against the veteran Italian who was bizarrely wearing a back brace on the outside of her shirt, before a tougher second set.
Third-seeded Grigor Dimitrov - who beat qualifier Dennis Novak 6-3, 6-2, 6-1 - No. 6 Marin Cilic, No. 10 Pablo Carreno Busta, No. 23 Gilles Muller, No. 24 Diego Schwartzman, No. 28 Damir Dzumhur, No. 30 Andrei Rublev and No. 31 Pablo Cuevas all advanced.
Venus took control in the next game putting the pressure back on the Swiss as a low ball in front of the net forced Bencic's volley to head well long to set up triple break back point.
It always shaped as a tough opener for Stephens, who hasn't won a tour-level match since her Grand Slam breakthrough triumph at the U.S. Open previous year and facing a player ranked No. 34, two spots off being seeded for the first major of the season. The 13 seed lost to 2-6, 7-6 (2), 6-2 to Zhang Shuai in her opener at Melbourne Park. "It's a long road and long season ahead". Stephens lost four matches in three tournaments in China, fell short in both her ties in the Fed Cup final.
Vandeweghe, a semi-finalist here and at the US Open past year, was handed two code violations during her defeat, the first of them after an argument with the umpire over a lack of bananas on court.
The 29-year-old German ended the year with tournament wins at Moscow and Zhuhai, then began 2018 with a win over Caroline Wozniacki in the final of the ASB Classic at Auckland, New Zealand.
A total 12 out of 15 American women and men in action lost on Day 1 at the Australian Open.
After tossing her racket, the 26-year-old appeared to scream obscenities toward Babos. The World No 78 Bencic sent shockwaves down the tournament and the draw with her win which saw her play with sheer confidence and outhit seven-time Grand Slam victor Venus.
Vandeweghe fought with umpire Fergus Murphy at the end of the first set after he called time and she remained in her chair to wait for a banana to be delivered.
Also out of the opening Grand Slam of the year is American big-hitter CoCo Vandeweghe, the 10th seed and a semi-finalist last year.
Bhambri is yet to win a round in the main draw of a Grand Slam and the Australian Open is the only Major he has played. Serena, of course, is on maternity leave so if nothing else the women's draw - also missing dual champion Victoria Azarenko, who is confined to California because of a child custody dispute - is more replete with possibility than might otherwise be the case.
Students of form would not have been too surprised by the 2-6, 7-6, 6-2 demise of 13th seeded Stephens to China's 34th-ranked Shuai Zhang; the 24-year-old had lost all seven of her matches since beating compatriot Madison Keys in NY to win her first grand slam on September 9.