The victory at St James' Park was the hosts' first in the Premier League this season after nine attempts and moved them off the bottom of the table ahead of their crunch derby against local rivals Sunderland next week.
Wijnaldum, 24, scored four goals in the match - only the second Newcastle player to do so in the Premier League after the league's record goal-scorer Alan Shearer.
Sissoko had a hand in four of his side's six strikes and was officially credited with three assists, McClaren claiming that showing proved why top clubs apparently want to sign him.
"The front four were excellent, especially Gini Wijnaldum," the head coach told Sky Sports.
"Individuals stepped up and that was the key thing.
"Moussa Sissoko showed strength and power and he showed why he is coveted by the top four. I thought the score could have been anything.
"We rode our luck and defended quite well. On the break we were terrific. I am relieved and the crowd got behind us from the first whistle.
"I am pleased for the players because it is been tough and hard. We had a tough week after [losing 6-1 to] Man City. We showed our strengths of what we are good at but we showed weaknesses by conceding two."
McClaren admitted there was little control from either side in a first half which saw five goals and almost constant attacking from both sides.
"What a game in the first half - I didn't know what was happening," he added to BBC Sport.
"We looked like scoring and conceding. We then settled down and produced some quality.
"We knew a win was around the corner, but we didn't know when it would come. We played some damn good football. We kept the faith with the players - everyone around us is saying what they have been saying, but we have got to keep tight.
"Against Chelsea and Man City we looked like scoring and here it was the same but the difference was we were clinical in our finishing."