The 26-year-old was handed the armband for the second time in his Reds career as Steven Gerrard was missing through injury.
He was on the scoresheet twice, and superbly helping to create the other three goals, which were claimed by Jordan Henderson, Jon Flanagan and Raheem Sterling.
There was just one change to the starting line-up, with Lucas Leiva returning to the team in the place of Gerrard.
The Reds were presented with a chance in the first minute, as the brilliant Suarez played in Philippe Coutinho, but the midfielder wasn't expecting the ball, and snatched at his shot.
The trend continued in the opening stanza, with Liverpool asking Spurs all kinds of questions in and around their box. Sterling was the creator-in-chief, bursting forward and getting the better of Kyle Naughton.
On 16 minutes, he skipped down the right channel and put pressure on Hugo Lloris' near post. In the next move, the winger got behind Spurs' defence again, but the French 'keeper averted the danger.
Suarez had seen an earlier effort go marginally wide, but there was no such repeat when Henderson slipped him in on 18 minutes.
Full report: Official Liverpool FC
Brendan Rodgers was left ruing a penalty that wasn't given as a Gareth Bale-inspired Tottenham prevailed 2-1 at White Hart Lane.
Fabio Borini made his debut and Steven Gerrard returned as Liverpool brought their tour of North America and Canada to a close with a 0-0 draw against Barclays Premier League rivals Tottenham at the M&T Bank Stadium in Baltimore.
Sky sources understand Tottenham are confident of signing Swansea and Liverpool target Gylfi Sigurdsson. 
Liverpool manager Brendan Rodgers wants Tottenham Hotspur and England Under-21 defender Steven Caulker to be his first signing at Anfield.
Liverpool FC long-term transfer target and want-away Barcelona playmaker, Ibrahim Afellay could be donning the red shirt of Merseyside. But with the Catalan giants ready to accept offers in the region of £6 million, Arsenal, Tottenham and Newcastle have all been alerted to the availability of Barcelona playmaker.
The grey and white tabby ran onto the field 11 minutes into the first half of the match at Anfield football stadium in Liverpool. It scampered toward Tottenham keeper Brad Friedel's goal and past Kop manager Kenny Dalglish before being scooped up by a steward and carried off the pitch.
Kenny Dalglish has admitted that he still has not forgotten about Liverpool's 4-0 hammering by Tottenham earlier in the season. 
The 26-year-old is one of a handful of players in the position to be linked with the Reds, as Kenny Dalglish considers his options following a season-ending injury picked up by Brazilian Lucas Leiva.
Sandro is frustrated at a lack of playing time at Spurs but they want him to stay as cover for Scott Parker.
The heavily tattooed Portuguese midfielder has seemingly fallen out of favour with Dalglish – he only came on a substitute during last Saturday's 1-1 draw with Sunderland at Anfield – and, given the club's excessive collection of central players, is now available for transfer.
It's now reported Sunderland are willing to pay £14million to take Aquilani off Liverpool's hands.
Liverpool boss Kenny Dalglish has already brought in Jordan Henderson from Sunderland this summer, but is looking to add further creative players to his squad.
Once the 40-year-old had opted not to move back to the continent, where he previously played for Turkish giants Galatasaray, that left him with four options in England.
