A game that had been meandering along amid much mediocrity came to life on the stroke of halftime when Can's extraordinary overhead scissors kick from Lucas's chipped through ball rocketed into the top corner.
The strike, hailed by the club's former defender Jamie Carragher as "one of the great Liverpool goals", illuminated a dull first-half which had just been enlivened by substitute Adam Lallana's dipping volley for the visitors that struck the bar.
An uninspired Watford side laboured for an equaliser after the break but still came agonisingly close when Sebastian Prodl smashed a left-foot shot against the bar for the Hornets in the 94th minute.
The victory strengthened Liverpool's hold on third place with 69 points, three points clear of fourth-placed Manchester City and four ahead of Manchester United, who are fifth.
The two Manchester sides, though, have a game in hand over their Merseyside rivals in the tense race for Champions league qualifying places.
"I have never scored a goal like that - maybe when I was younger. That is the best goal I've ever scored," the exultant Can told Sky Sports.
"I saw the space and I ran behind and my first thought was that I wanted to head it, then I didn't think too much.
"Everything is now in our hands. If we win the (last) three games we are in the Champions League. We are confident. If we perform how we can perform then we can do it."
The goal from the German international was unquestionably one of the best seen in the Premier League in 2016-17 but what felt most remarkable about it was that it materialised after such an undistinguished performance from Juergen Klopp's team.
When Liverpool lost playmaker Philippe Coutinho to a leg injury suffered after a fourth minute challenge, there was little cohesion or punch in their approach.
Then, from seemingly nowhere, the Brazilian's replacement Lallana uncorked a moment of inspiration five minutes before the break.
From goalkeeper Heurelho Gomes' punched clearance, England international Lallana blasted his first-time 20-metre volley against the underside of the bar.
It was just the hors d'oeuvre, though. In stoppage time in the first half, Lucas, whose only contribution hitherto had been to get booked for a terrible dive, floated his through ball into the area where Can set himself for a moment of acrobatic wonder.
With no element of fluke, he twisted his body in mid-air to hook the ball flush on his right foot past a bewildered Gomes and sparked huge celebrations on the Liverpool bench.
"This bicycle (kick) was pretty special, really wonderful," Klopp said.
It looked like a settler for Liverpool, who have so often blown victory opportunities against the league's lesser sides this season while excelling against their fellow top-six contenders.
Yet though Lallana came close to scoring on the break, and substitute Daniel Sturridge forced a wonderful late save from Gomes in the dying seconds, Liverpool's failure to close out the game almost cost them.
In the last of four extra minutes, they failed to clear their lines and Prodl lashed his shot against the bar with Watford's final attack.
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