The summer signings struck either side of a powerful Martin Skrtel header as the hosts, inspired by the outstanding Luis Suarez, produced an electrifying performance at Anfield.
Bolton struck late on through Ivan Klasnic but generally offered little as Liverpool, backed by a raucous crowd, displayed further evidence of their rejuvenation under Kenny Dalglish.
The home team maintained a ferocious tempo from the kick-off with Suarez, preferred to Andy Carroll up front, at the heart of almost all their attacking play.
With Henderson and Stewart Downing also influential, Liverpool looked a different proposition from the Roy Hodgson side which started the last campaign so sluggishly.
For Bolton, defeat was a reality check after a promising start to the season. It may also have been their last game with Gary Cahill as Arsenal consider whether to make another bid for the inspirational defender before Wednesday's transfer deadline.
Bolton struggled to cope with the pace of Liverpool from the outset and were fortunate to survive when Downing lost control in the area after a quick counter-attack.
It came as little surprise, then, when the Reds claimed the lead after more good work in the 15th minute.
Suarez brilliantly crossed into the box with the outside of his left boot and Jussi Jaaskelainen reacted quickly to keep out Downing's volley.
Dirk Kuyt was first to the loose ball and fed Henderson who, after his first effort was blocked by Nigel Reo-Coker, fired firmly into the top corner.
Bolton almost grabbed a spectacular equaliser moments later when Chris Eagles crossed for Martin Petrov but Jose Reina parried the Bulgarian's tight-angled volley.
Liverpool upped the tempo with Suarez driving forward and Kuyt almost diverting in a low cross in from close range. Suarez then broke clear and coolly lobbed Jaaskelainen but the ball dropped just over the bar.
Both sides were forced to reorganise midway through the first half. Bolton sent on Mark Davies after Fabrice Muamba went off before Liverpool right-back Martin Kelly, who missed the closing months of last season, left the action to be replaced by Skrtel.
Suarez delivered another dangerous cross soon after but Kuyt volleyed straight at Jaaskelainen from a Downing flick-on.
Kuyt then went close from long range before the Reds appealed for a penalty when Gretar Steinsson handled as Downing tried to flick the ball past him.
Replays, however, backed referee Lee Probert's decision to give a free-kick just outside the box, and Henderson's cross was subsequently cleared.
Liverpool maintained the pressure after the break and within moments of the restart Suarez was clear again.
The Uruguayan broke into the box but his fall after an attempted challenge by Zat Knight was theatrical.
Suarez, with countryman and prospective new signing Sebastian Coates watching in the main stand, was then involved in the action again on the edge of the area.
He was bundled off the ball but Adam picked up possession and had a shot deflected wide. The Scot took the resulting corner himself and delivered an inviting cross for Skrtel to double the lead with a thumping header.
Adam got on the scoresheet barely a minute later as he finished off good work from Kuyt by firing low past Jaaskelainen.
It almost got worse for Bolton as Suarez rounded Jaaskelainen but shot into the side-netting.
Bolton had a rare opportunity when Klasnic had a shot blocked by Jamie Carragher but there was little respite for the Trotters as Daniel Agger charged forward from deep to fire a shot well over.
Liverpool should have had a free-kick inside the area when Jaaskelainen clearly handled a back-pass from Paul Robinson under pressure from Suarez but Probert gave nothing.
Suarez and Henderson made way for Carroll and Maxi Rodriguez 14 minutes from time.
The Reds eased off but continued to dominate possession with Jose Enrique twice finding room to whip in good crosses.
Some of the gloss was taken off their afternoon, however, when Petrov troubled Carragher and Klasnic tapped in a stoppage-time consolation.
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