The midfielder provided the assist for the winning goal before producing a tireless performance to help Arsenal protect their lead.
The victory was Arsenal's first Premier League win at Anfield since 2012 and moved Mikel Arteta's side three points clear at the top of the table.
Named Player of the Match, Rice was delighted to finally celebrate a victory at a stadium where he has previously experienced difficult afternoons.
"Coming to Anfield, I think the record here speaks for itself â- the first win here in 14 years," Rice said.
"To win 1-0, to show that togetherness and resilience, it's unbelievable. I'm just delighted to get the win and the three points."
Rice revealed that Arteta had made ending Arsenal's long wait for an Anfield victory a major focus of the pre-match preparations.
"The manager drilled that into us. He showed us the last time before we won at Spurs away and Chelsea away, it was many, many years, and Liverpool was the longest outstanding one," he explained.
"He drilled it into us to have that mentality to come here today and win, to show that togetherness."
The England international also praised the unity within the Arsenal squad, crediting Arteta for creating an environment where players enjoy working together.
"I think the togetherness is unmatched. I've never been in a team like it that's got this togetherness," he said.
"The manager, what he's built, how happy everyone is every day to come in, see each other, work and represent this club â- it's amazing."
Rice admitted the victory was particularly satisfying after previously suffering disappointing results against Liverpool at Anfield.
"To come and win today, put in a really good performance against a top side who are doing really, really well, I'm delighted," he added.
Arsenal also responded positively to Tuesday's disappointing defeat by Fleetwood, with Rice highlighting the importance of bouncing back quickly.
"After Tuesday it felt like the world had come crashing down, losing to Fleetwood, but then to have the reaction like this â- that's the beauty of football," he said.
"You always have one the week after to put things right, and we've done that today and made Arsenal fans very happy."
Arsenal now turn their attention to the UEFA Champions League, where they face Slavia Prague at the Fortuna Arena on Wednesday.