Olivier Ntcham's goal just after the hour mark settled a game in which the Hoops struck the frame of the goal four times.
'Steven has done a great job going into there, he's got the team organised and they are threat, but I thought today we were excellent.
Celtic moves up to second in the table, three points behind Hearts, which has won all four of its games.
Celtic could count itself unfortunate not to have already been ahead as a spell of extreme pressure before half time saw both Forrest and Mikel Lustig strike the crossbar.
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Despite the 1-0 loss to Celtic on Sunday, Rangers' defending was much improved at Parkhead.
The second-half followed a similar pattern to the first-period with Celtic carving out the better opportunities and they finally opened the scoring in the 62nd minute when Ntcham put the finishing touches to a nice move after a mazy run from Tom Rogic. It's a classic goal on the counter-attack, finished off by Ntcham.
Steven Gerrard has hit the ground running in his management career with Rangers, enjoying an unbeaten start to life in Scotland.
The Rangers manager also believes there was a foul in the build up to Celtic's goal.
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Even when Celtic took the lead and Rangers pushed more, Gerrard's men hardly looked like troubling their opposition defence with simple passes in attack not working out.
Rangers were in action in Russian Federation on Thursday and had to play with just nine men for a portion of the game, and Gerrard opted to sit back off Celtic at Parkhead.
But in the Old Firm derby, Boyata was solid in defence when called upon to gave Alfredo Morelos very little room to hurt Celtic's back line.
Though Gerrard's arrival in the summer has brought many positive changes to Rangers, the Glasgow side have one thing they still need to work on. Allan McGregor had to make some decent stops, but Celtic were largely restricted considering their possession. After Caixinha was propelled through the exit, Murty took over again for a passage which ended amid a Celtic blitz - 4-0 in the Scottish Cup semi-final and 5-0 on the day Rodgers and Co claimed last season's title.
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Kilimnik also is a co-defendant in a pending case against Manafort in Washington that accuses them both of witness tampering. Patten's personal website describes him as a "strategic advisor" who has worked in politics on four continents.