The right-back netted eight minutes from time to secure a point for the Hoops against the Scottish Premiership table-toppers, who had raced into a two-goal lead through first-half strikes from Aaron Doran and Richie Foran.
But Charlie Mulgrew replied following the interval and Matthews grabbed the equaliser towards the end.
Matthews believes that more of the same will serve Celtic well as they seek to overturn a 2-0 first-leg deficit against the Kazakhstan champions at Parkhead on Wednesday night.
He said: “We are confident we can get the result we need.
“We showed in the first leg that we can cause them problems going forward. We just need to keep it solid at the back.
Elsewhere 10-man Hearts overcame Aberdeen 2-1 and reduced their administration-imposed 15-point deficit to -8 thanks to Jordan McGhee’s 88th-minute winner.
Edinburgh rivals Hibernian came away from Kilmarnock with a 2-1 win while Dundee United thrashed St Johnstone 4-0 in the Tayside derby.
John Sutton was on target for Motherwell as they beat Partick Thistle 1-0 at Fir Park and finally two Richard Brittain goals helped Ross County see off St Mirren 3-0 at Victoria Park.