Williamson and Perch deputised at centre-back for the visit of Kenny Dalglish’s men due to injuries to captain Fabricio Coloccini and Steven Taylor.
The duo were able to keep Luis Suarez and former Tyneside favourite Andy Carroll at bay as they registered a clean sheet, and the 28-year-old says that their relationship made the difference.
"Me and James are close and I think that showed [on Sunday]," Williamson told BBC Newcastle.
"We've got each other's back in the game - [and] it's always pleasing to keep a clean sheet against that quality."
|"Me and James are close and I think that showed [on Sunday] - we've got each other's back in the game"
- Mike Williamson on James Perch
The defender went on to praise two-goal hero Papiss Cisse, who took his Premier League tally to seven strikes in as many games with a double at Sports Direct Arena against the Reds.
The Senegal international has been a revelation since joining the Magpies from Freiburg in January, with his all-round play and high work-rate impressing his team-mate the most.
"He's a fantastic outlet," Williamson enthused.
"He's got the quality to score some of the goals that you've seen, which is a brilliant thing to have.
||Newcastle are 15/4 to be the only team to score when they play Swansea City on Friday
Newcastle are now level on points with Chelsea after their third win in succession and the ex-Portsmouth man believes that the squad have the togetherness to continue their push for European qualification.
"We've got that momentum, it's just what we've been doing all season," he observed.
"We've got honest lads, we work hard and we play for each other which I think is a good mix to have."