A topsy-turvy encounter at the Wankdorf Stadium saw both sides hold the lead before the Premier League outfit eventually prevailed to seal a win, with the 20-year-old on form.
Juhani Ojala's bizarre own-goal gave the Reds the lead in the fourth minute but Young Boys fought back and a defensive lapse allowed Raphael Nuzzolo to equalize but Andre Wisdom's header soon after restored the Reds' lead.
Young Boys pushed on in the second half, Ojama made amends for his earlier mishap with a goal of his own before Gonzalo Zarate turned the game on its head, but Sebastian Coates equalized from a corner before Jonjo Shelvey scored twice to seal three points for the Premier League outfit.
Brendan Rodgers made eight changes to the side that drew at Sunderland last weekend, including appearances for youngsters Dani Pacheco, Suso and Wisdom, as well as handing Nuri Sahin a start in midfield.
The Reds got off to the best possible start, albeit in freakish circumstances. Downing's cross from the right looked non-threatening but Christoph Spycher's clearing header hit Ojala in the face and trickled past a helpless Marco Wolfi in the Young Boys goal.
The home side looked to get back into the tie quickly, Raul Bobadilla turned Jamie Carragher with ease before drawing a save from Brad Jones and Alexander Farnerud also got better of the 34-year-old before tumbling in the box, but not receiving a penalty.
Eventually, Young Boys broke down the Reds' defense, Bobadilla and Farnerud combining to move down the pitch. Jose Enrique shut the Argentine down, with the ball bobbling towards Jones, however, the Spaniard inexplicably took the ball past his keeper and could only scuff his clearance to Nuzzolo, who finished into the unguarded net.
The parity lasted less than three minutes, Enrique stormed down the left and won a corner, which was whipped by Sahin onto the head of Wisdom, who powered home a debut goal.
The last of the first-half action saw Farnerud slap the post with a 25-yard effort that was curled around Carragher, but the sides went in at the break with Liverpool ahead.
The home side got back on level terms for a second time, however, just seven minutes into the half as Liverpool failed to clear a corner fully and Bobadilla's cross was flicked home by Ojama, who found the net for the second time in the game.
Rodgers' response was to replace the inexperienced and ineffective Pacheco with Fabio Borini in an attempt to take the lead for the third time.
It backfired however, as a lightning counterattack by the home side following a Reds corner saw the powerful Bobadilla release Zarate down the right flank, where he took a touch before dinking a delightful finish over the onrushing Jones.
The topsy-turvy contest took another twist just six minutes later. Borini saw a one-on-one saved and from Downing's resulting corner, Coates leaped above Ojama and looped a header into the far corner, with the Italian making life difficult for the defenders on the line.
The goals continued with 75 minutes on the clock. Young Boys' Elsad Zverotic played a blind back-pass straight to Borini, the Italian bursting forward before switching play to Henderson who slipped the ball to substitute Shelvey. The 20-year-old tucked home from 12 yards.
With the home side pushing forward, Liverpool sealed the win with just five minutes remaining. Shelvey slalomed his way through a couple of tackles before blasting a left-footed effort past Wolfi to secure the three points.
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